Question

# The random variables X Y f XY xyax^xyx 0 otherwise   Find the constant a

and are distributed according to the joint PDF

,(,) = {2 if 1≤≤2 and 0≤,

1. Determine the marginal PDF fY(y)

a. If 0≤y≤1

b. if 1<y≤2

1. Determine the conditional expectation of 1/((X^2)*Y), given that Y=5/4

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Question 2:

You have to integrate ﻿﻿ with respect to x to get the marginal PDF of Y. The range of x is tricky. But we know that ﻿﻿ . So ﻿﻿ and also ﻿﻿ . Combining the two gives ﻿﻿ So integrate ﻿﻿ with respect to x with the limits y to 2.

Also remember that since in both a and b ﻿﻿ , the answer will be the same.

Question 3:

You can substitute ﻿﻿ in the expression ﻿﻿ . Then,

﻿﻿ ﻿﻿. The denominator we have from part 2. This should be a simple integration now.