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Q: Would like to clearly understand and solve this example from Probability and Statistical Inference with...

Q: Would like to clearly understand and solve this example from Probability and Statistical Inference with the steps of the solution to better understand, thanks.

**Please explain and give the step by step with details to completely see how the solution came about, plenty of thanks.

1) a) Let X1, X2 denote two independent random variables, each with a χ2 (3) distribution. Find the joint p.d.f. of Y1=X1 and Y2=X2+X1. Here note that the support of Y1, Y2 is 0 1 < y2 < ∞. Also find the marginal p.d.f. of each of Y1 and Y2. Are Y1 and Y2 independent?

b) Find the joint pdf of Y1 = X1 + X2,   Y2 = X1 + X2.

c) Find the marginal pdf of Y1.

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