Question

Let X1 and X2 have the joint pdf f(x1,x2) = 8x1x2    0<x1 <x2 <1 0....

Let X1 and X2 have the joint pdf

f(x1,x2) = 8x1x2    0<x1 <x2 <1

0. elsewhere

  1. What are the marginal pdfs of x1 and x2?

  2. Find the expected values of x1 and x2.

3.   What is the expected value of X1X2? (Hint: Define g(X1, X2) = X1X2 and extend the definition of expectation of function of a random variable to two variables as follows: E[g(X1, X2)] = ? ? g(x1, x2)f(x1, x2)dx1dx2.

4. Suppose that Y = X1/X2. What is E(Y)? (Same as above)

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