Probability

Mr Pandazis Practice Questions for Test #3 Math 241 These are only practice questions. The actual test may be different. Test 3 is on Chapter 6 material and joint probability density functions in Chapter 7. 1. If X is the maximum of the numerical outcomes of two rolls of a die, and Y is the number of tails in one coin toss, what is the joint probability density function of X and Y? 2. Let X be a discrete random variable with probability function f(x) given by f(3) = and f(5) = Z.Find E(X? + 3X +9). 3. Let X be a continuous random variable with pdf f(x) = {[}e Tifx=20 0 elsewhere Find E(X). 4. Suppose that a point (X,Y) is selected at random from inside the circle with radius 3 and center at (0,0). Find the joint pdf of Xand Y. 5. Prove that Var(aX + b) = a*Var(X). 6. Provethat Var(X) = E(X?) E*(X)