To Whom This May Concern,

I'm stuck on the following homework questions as shown in the picture. Please help guide me. Thank you!

1. Let X have the standard normal pdf, fx(x) = (1/(sqrt(2pi))e^(-x^2)/2 , -infinity

a) Find the pdf of Y = |X|

b) Find the E(Y).

2.Let X have the pdf: f(x) = (1/2) (1+x), -1

a) Find the pdf of Y = X^2

b) Find E(Y) and Var(Y)

Additional problems

1.Consider the rolling of a fair six-sided die, let X represent the number on the uppermost face, find the E(X) and Var (X)

2.Suppose that Y ~ exponential

3.Let the continuous random variables (X, Y) have joint pdf:

I. Textbook Problems (Casella and Berger 2"d Ed ) : 2.11. (2 points) Let X have the standard normal pdf, fx(x) = (1/V2n)e /2, - c0 0. Let U = VY. Find the pdf of U. 3. (2 points) Let the continuous random variables (X, Y) have joint pdf : fxy (x, y) = (ye(-xy), if 0