Let X1, X2 denote two independent random variables, each

Chapter 5, Problem 1E

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QUESTION:

Problem 1E

Let X1, X2 denote two independent random variables, each with a χ2(2) distribution. Find the joint pdf of Y1 = X1 and Y2 = X2 + X1. Note that the support of Y1, Y2 is 0 < y1 < y2 < ∞. Also, find the marginal pdf of each of Y1 and Y2. Are Y1 and Y2 independent?

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QUESTION:

Problem 1E

Let X1, X2 denote two independent random variables, each with a χ2(2) distribution. Find the joint pdf of Y1 = X1 and Y2 = X2 + X1. Note that the support of Y1, Y2 is 0 < y1 < y2 < ∞. Also, find the marginal pdf of each of Y1 and Y2. Are Y1 and Y2 independent?

ANSWER:

Step 1 of 4

Given data

Both the independent variables are in  distribution

                                               

                                               

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