Hi, I have questions.

I need your help.

Thanks.

Q1:

You have two dice, one with three sides labeled 0,1,2 and one with 4 sides, labeled 0, 1, 2, 3. Let X1 be the outcome of rolling the first die, and X2 the outcome of rolling the second. The rolls are independent. a. What is the joint distribution of (X1, X2)? b. Let Y1 = X1 . X2 and Y2 = max {X1, X2). Make a table for the joint distribution of Y1, Y2. c. What are the marginal distribution of Y1, Y2? Are they independent?Let X be a non-negative random variable taking values in {1, ..., 100}. Show that 100 E( X = P( X z n). n=1 Hint: Take In = 1 if X > n and In = 0 if X 0, y > 0 0 otherwise fX,Y(x7y) :{ (a) What is the value of C? (b) Find the marginal probability density function fy. Can you identify this random variable? Hint: Look up Gamma random variable from Lecture notes / book