Calculate probability P ( F − ) and explain its meaning.

Question

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Answer 1

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

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Answer 2

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

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Answer 3

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

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Answer 4

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

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Answer 5

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Answer 6

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Answer 7

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

Answer 8

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Answer 9

i.

Expert Solution

Answer 10

i.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Answer 13

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Answer 14

ii.

To determine

Calculate probability P(A+) and explain its meaning.

Answer 15

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Answer 16

ii.

Expert Solution

Answer 17

ii.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Answer 20

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Answer 21

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

Answer 22

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Answer 23

iii.

Expert Solution

Answer 24

iii.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Answer 27

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Answer 28

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

Answer 29

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Answer 30

iv.

Expert Solution

Answer 31

iv.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Answer 34

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Answer 35

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

Answer 36

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Answer 37

v.

Expert Solution

Answer 38

v.

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Answer 41

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Answer 42

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

Answer 43

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Answer 44

vi.

Expert Solution

Answer 45

vi.

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.