Problem # 9. An attempt to establish a video call via some social media app may fail with probability 0.1. If connection is established and if no connection failure occurs thereafter, then the duration of a typical video call in minutes is an exponential random variable X with E[X] = 3. However, due to an unfortunate bug in the app all calls are disconnected after 6 minutes. Let random variable Y denote the overall call duration (i.e., Y = 0 in case of failure to connect, Y = 6 when a call gets disconnected due to the bug, and YX otherwise.) Find: a) Fy(y) b) fy(y) c) E[Y] d) στ