Let X be a random variable with u = 4 and o = .5. (a) Use the Chebychev inequality to estimate Pr(3 s X < 5).

Let Y be a Poisson random variable with mean λ = 2. (a) Find P(Y ≥ 2). (b) Find P(Y ≥ 4|Y ≥ 2).

With reference to Definition 4, show that μ0 = 1and that μ1 = 0 for any random variable for whichE(X) exists.

We have a random variable X and Y that jave the joint pdf f(x) = {1    0<x<1, 0<y<1}                                                                                                                                                          {0         otherwise} Let U = Y - X2.  What is the support for the random variable U? Are there critical points? If  U = Y/X.       What is the support for the random variable U? Are there critical points?