Suppose that Y1 and Y2 are jointly distributed with joint pdf: f(y1,y2) ={cy2. for 0 ≤...

Suppose that Y1 and Y2 are jointly distributed with joint pdf:

f(y1,y2) ={cy2. for 0 ≤ y1 ≤ y2 ≤ 1

0. otherwise}

(1) Find c value.

(2) Are Y1 and Y2 independent? Justify your answer.

(3) ComputeCov(Y1,Y2).

(4) Find the conditional density of Y1 given Y2=y2.

(5) Using (d), find the conditional expectation E (Y1|Y2).

(6) Suppose that X1=Y1+Y2, and X2= 2Y2. What is the joint density ofX1andX2?

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orchestra answered 1 year ago

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