Problem # 1. Outside the airport terminal, at the shuttle stop, you sometimes wait a long time for the right shuttle that will take you to your hotel. You are quite annoyed to see many other shuttle vans passing. Suppose the total number of shuttle vans N you see passing, until at last you board the right one, is a geometric random variable with parameter p = 0.02. What is the probability P[N > 100]...? Problem # 2. Show that the CDF of a geometric random variable with parameter p can be expressed as Ex(x) = { 0. x < 1 1- (1 - p)] x ≥1 where [x] denote the floor function, or the largest integer k such that k ≤ x. Problem # 3. A video server sends a packet containing a video frame to a user. The packet is received correctly with probability p, in which case the server receives prompt acknowledgment. If it does not receive acknowledgment within a predefined interval of time T the server sends it again, and again after another T, etc., until acknowledgment is received. However, real-time streaming only allows up to six such attempts before the server must abandon this frame and move to the next one. Let random variable X be the number of attempts made by the server for a given video frame. Find the CDF Fx(x).