If X and Y are both discrete, show that Ex Pxir(xy) 1 for all y such that py(y) > 0.

2. Let X, and X be independent geometric random variables having the same parameter p. Guess the value of Hint: Suppose a coin having probability p of coming up heads is continually flipped. If the second head occurs on flip number n, what is the conditional probability that the first head was on flip number i, i=1,...,n-1? Verify your guess analytically.