Graph for density function.

Question

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Answer 1

Question

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

(b)

To determine

Probability of X that lies between 1 and 3.

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

(c)

To determine

Probability of X that lies between 4 and 8.

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

(d)

To determine

Estimate the probability of X less than 7.

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

(e)

To determine

Estimate the probability that X is greater than 3.

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

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Answer 2

Question

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

(b)

To determine

Probability of X that lies between 1 and 3.

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

(c)

To determine

Probability of X that lies between 4 and 8.

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

(d)

To determine

Estimate the probability of X less than 7.

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

(e)

To determine

Estimate the probability that X is greater than 3.

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

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Answer 3

Question

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

(b)

To determine

Probability of X that lies between 1 and 3.

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

(c)

To determine

Probability of X that lies between 4 and 8.

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

(d)

To determine

Estimate the probability of X less than 7.

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

(e)

To determine

Estimate the probability that X is greater than 3.

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

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Answer 4

Question

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

(b)

To determine

Probability of X that lies between 1 and 3.

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

(c)

To determine

Probability of X that lies between 4 and 8.

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

(d)

To determine

Estimate the probability of X less than 7.

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

(e)

To determine

Estimate the probability that X is greater than 3.

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

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Answer 5

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

(b)

To determine

Probability of X that lies between 1 and 3.

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

(c)

To determine

Probability of X that lies between 4 and 8.

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

(d)

To determine

Estimate the probability of X less than 7.

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

(e)

To determine

Estimate the probability that X is greater than 3.

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

Answer 6

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

Answer 7

Chapter 8.1, Problem 13E

(a)

To determine

Graph for density function.

Answer 8

(a)

Expert Solution

Explanation of Solution

Suppose the given density function is F(X)={X25; (0<x<5)10−X25; (5<x<10).

The density function can be represented as follows:

EBK STATISTICS FOR MANAGEMENT AND ECONO, Chapter 8.1, Problem 13E

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

Probability of X that lies between 1 and 3.

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

Answer 13

(b)

To determine

Probability of X that lies between 1 and 3.

Answer 14

(b)

Expert Solution

Explanation of Solution

The probability of X that lies between 1 and 3 can be obtained as follows:

P(1<X<3)=P(X<3)−P(X<1)=12×325×(3−0)−12×125×(1−0)=0.18−0.2=0.16

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

(c)

To determine

Probability of X that lies between 4 and 8.

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

Answer 19

(c)

To determine

Probability of X that lies between 4 and 8.

Answer 20

(c)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(4<X<8)=P(4<X<5)+P(5<X<8)......(1)P(4<X<5)=P(X<5)−P(X<4)=12×525×(5−0)−12×425×(4−0)=0.5−0.32=0.18P(5<X<8)=P(X>5)−P(X>8)=12×525×(10−5)−12×225×(10−8)=0.5−0.8=0.42

Substitute the values in the above Equation (1).

P(4<X<8)=P(4<X<5)+P(5<X<8)=0.18+0.42=0.60

Answer 21

(c)

Expert Solution

Answer 22

(c)

Expert Solution

Answer 23

Expert Solution

Answer 24

(d)

To determine

Estimate the probability of X less than 7.

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

Answer 25

(d)

To determine

Estimate the probability of X less than 7.

Answer 26

(d)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X<7)=1−P(X>7)P(X>7)=12×325×(10−7)=0.18P(X<7)=1−0.18=0.82

Answer 27

(d)

Expert Solution

Answer 28

(d)

Expert Solution

Answer 29

Expert Solution

Answer 30

(e)

To determine

Estimate the probability that X is greater than 3.

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

Answer 31

(e)

To determine

Estimate the probability that X is greater than 3.

Answer 32

(e)

Expert Solution

Explanation of Solution

The probability can be estimated as follows:

P(X>3)=1−P(X<3)P(X<3)=12×325×(13−0)=0.18P(X>3)=1−0.18=0.82

Answer 33

(e)

Expert Solution

Answer 34

(e)

Expert Solution

Answer 35

Expert Solution

Answer 36

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Graph for density function.

Graph for density function.

Explanation of Solution

Probability of X that lies between 1 and 3.

Explanation of Solution

Probability of X that lies between 4 and 8.

Explanation of Solution

Estimate the probability of X less than 7.

Explanation of Solution

Estimate the probability that X is greater than 3.

Explanation of Solution

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Chapter 8 Solutions