Question: For the following density function where X and Y are independent. f(x) = { x(1+3y 2 ) 4 , 0 < x < 2, 0

For the following density function where X and Y are independent.

f(x) = { x(1+3y 2 ) 4 , 0 < x < 2, 0 < y < 1

0, elsewhere

1. Confirm that f(x, y) is a probability distribution

2. Find F(x)

3. Find E(X)

4. Find E(Y )

5. Find E(X/Y )

6. Find 2 X (sigma sq. x)

7. Find 2 Y (sigma sq. y)

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