Two random variables, X and Y, have joint probability density function f ( x , y...

Question

Question

Two random variables, X and Y, have joint probability density function

f ( x , y ) = { c , x < y < x + 1 , 0 < x < 1

0 , o t h e r w i s e

Find c value.
What's the conditional p.d.f of Y given X = x, i.e., f Y ∣ X = x ( y ) ? Don't forget the support of Y.
Find the conditional expectation E [ Y | X ].
Find the joint p.d.f of V = X and W = Y − X.
Are V and W are independent? Justify your answer.
Find the cumulative distribution function of W. Which named distribution is this?

math Statistics-And-Probability

Answer 1

Answer #1

Answer 2

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