(a) To find: The outcomes of the experiment.

Question

1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.

Answer 1

Question

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

To determine

(c)

To find:

The probability distribution of the random variable.

To determine

(d)

To draw:

The histogram representing this distribution.

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1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.

Scenario Sales of products by color follow a peculiar, but predictable, pattern that determines how many units will sell in any given year. This pattern is shown below Product Color 1995 1996 1997 Red 28 42 21 1998 23 1999 29 2000 2001 2002 Unit Sales 2003 2004 15 8 4 2 1 2005 2006 discontinued Green 26 39 20 22 28 14 7 4 2 White 43 65 33 36 45 23 12 Brown 58 87 44 48 60 Yellow 37 56 28 31 Black 28 42 21 Orange 19 29 Purple Total 28 42 21 49 68 78 95 123 176 181 164 127 24 179 Questions A) Which color will sell the most units in 2007? B) Which color will sell the most units combined in the 2007 to 2009 period? Please show all your analysis, leave formulas in cells, and specify any assumptions you make.

5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}

Answer 2

Question

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

To determine

(c)

To find:

The probability distribution of the random variable.

To determine

(d)

To draw:

The histogram representing this distribution.

Expert Solution & Answer

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Answer 3

Question

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

To determine

(c)

To find:

The probability distribution of the random variable.

To determine

(d)

To draw:

The histogram representing this distribution.

Expert Solution & Answer

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Answer 4

Question

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

To determine

(c)

To find:

The probability distribution of the random variable.

To determine

(d)

To draw:

The histogram representing this distribution.

Expert Solution & Answer

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Answer 5

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

To determine

(c)

To find:

The probability distribution of the random variable.

To determine

(d)

To draw:

The histogram representing this distribution.

Answer 6

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

Answer 7

Chapter 8.CRE, Problem 1CRE

To determine

(a)

To find:

The outcomes of the experiment.

Answer 8

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

Answer 9

To determine

(b)

To find:

The value assigned to each outcome of this experiment.

Answer 10

To determine

(c)

To find:

The probability distribution of the random variable.

Answer 11

To determine

(c)

To find:

The probability distribution of the random variable.

Answer 12

To determine

(d)

To draw:

The histogram representing this distribution.

Answer 13

To determine

(d)

To draw:

The histogram representing this distribution.

Answer 14

Expert Solution & Answer

Answer 15

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Ch. 8.1 - What is a random variable? Give an example.Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Three balls are selected at random without...Ch. 8.1 - 2.A coin is tossed four times. Let the random...Ch. 8.1 - A die is rolled repeatedly until a 6 falls...Ch. 8.1 - Cards are selected one at a time without...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

(a) To find: The outcomes of the experiment.

Solution Summary: The author explains that an urn contains 3 white balls and 4 blue balls in that, 3 balls are selected at random without replacement.

(a)

To find:

The outcomes of the experiment.

(b)

To find:

The value assigned to each outcome of this experiment.

(c)

To find:

The probability distribution of the random variable.

(d)

To draw:

The histogram representing this distribution.

Chapter 8 Solutions

(a) To find: The outcomes of the experiment.

Solution Summary: The author explains that an urn contains 3 white balls and 4 blue balls in that, 3 balls are selected at random without replacement.

(a) To find: The outcomes of the experiment.

(b) To find: The value assigned to each outcome of this experiment.

(c) To find: The probability distribution of the random variable.

(d) To draw: The histogram representing this distribution.

Chapter 8 Solutions

(a)

To find:

The outcomes of the experiment.

(b)

To find:

The value assigned to each outcome of this experiment.

(c)

To find:

The probability distribution of the random variable.

(d)

To draw:

The histogram representing this distribution.