1.

Assume that random variables X and Y have joint probability density function given by f(x,y) = (1/24) x² y² where 0 <= x <= 3 and 0 <= y <= 2 and is zero elsewhere. What is the marginal density of X?

Group of answer choices

f(x) = x^2

f(x) = (1/24)*(x^2)

f(x) = (1/9)*(x^2)

f(x) = (1/72)*(x^3)

f(x) = (1/24)*(x^3 -9)

2.

Using the information obtained in question 2, what is the conditional expectation of X given Y=1.5 i.e. E(X | Y=1.5)?

Group of answer choices

1.90

1.50

2.57

2.25

.27

3.

Using the information in question 1, what is V(5X +3Y)?

Group of answer choices

9.79

.49

2.26

2.14

3.90