Create an expression for the joint density of X + Y and X − Y .

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Answer 1

Question

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

b.

To determine

Create an expression for the joint density of XY and YX.

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

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Suppose that two continuous random variables X and Y have joint probability density function fxy = A( ex+y + e2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3 0 elsewhere a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0

Let X and Y be two independent random variables, X ∼ Γ(α, λ) and Y ∼ Γ(β, λ). Find the joint probability density function f(Z,W)of the vector (Z, W)(b) Show that Z and W are independent(c) Show that Z ∼ Γ(α + β, λ) and W ∼ B(α, β)

Let X and Y be a pair of continuous random variables with a joint density fx,y(x,y). Assume that fx,y(x,y) = cxy for x greater than or equal to 0, y greater than or equal to 0, and x + y less than or equal to 1. Here c is a constant. Assume that fx,y(x,y) is 0 elsewhere. What is the constant c equal to? With the value of c, what is E[XY]?

Answer 2

Question

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

b.

To determine

Create an expression for the joint density of XY and YX.

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

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Answer 3

Question

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

b.

To determine

Create an expression for the joint density of XY and YX.

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

b.

To determine

Create an expression for the joint density of XY and YX.

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

b.

To determine

Create an expression for the joint density of XY and YX.

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

Answer 6

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

Answer 7

Chapter 3.8, Problem 63P

a.

To determine

Create an expression for the joint density of X+Y and X−Y.

Answer 8

b.

To determine

Create an expression for the joint density of XY and YX.

Answer 9

b.

To determine

Create an expression for the joint density of XY and YX.

Answer 10

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

Answer 11

c.

To determine

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 3.8 - Prob. 1P Ch. 3.8 - Prob. 2P Ch. 3.8 - Prob. 3P Ch. 3.8 - Prob. 4P Ch. 3.8 - Prob. 5P Ch. 3.8 - Prob. 6P Ch. 3.8 - Prob. 7P Ch. 3.8 - Prob. 8P Ch. 3.8 - Prob. 9P Ch. 3.8 - Prob. 10P

Create an expression for the joint density of X + Y and X − Y .

Create an expression for the joint density of X+Y and X−Y.

Create an expression for the joint density of XY and YX.

Specialize the expressions from parts (a) and (b) to the case where X and Y are independent.

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