The random variables X and Y have joint PDF given by:

f(x, y) =(1/(10)), (x,y)∈[-1,1] ×[-2, 2] ∪ [1, 2] ×[-1,1]

(a) Find the conditional PDFs f(y\x) and f(x\y)

(b) Find E[X\Y ], E[X] and var(X\Y ). Use these to calculate var(X).

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- September 7th 2010, 02:57 AMulysses123conditional Joint PDF's
The random variables X and Y have joint PDF given by:

f(x, y) =(1/(10)), (x,y)∈[-1,1] ×[-2, 2] ∪ [1, 2] ×[-1,1]

(a) Find the conditional PDFs f(y\x) and f(x\y)

(b) Find E[X\Y ], E[X] and var(X\Y ). Use these to calculate var(X).