A communication system has 2 subsystems connected in series. Subsystem A has Link #1 connected in series with link #2. These two links are connected in parallel with link #3. The second subsystem contains only a single link, Link #4. Each link may fail or not fail independently of the other links in a given interval of time. Define the events F = {Link #i functioning}, Assume that all links have a probability of failure of 0.01. i = 1,2,3,4 (a) Determine the probability of failure of the communication system. (5 marks) (b) Determine the probability that link #1 is functioning given that the communication system is functioning properly. (3 marks) == (c) Let M, denote the capacity of link #i in megabits per second, and assume that M = M = 10, M2 8 and M3 = 4. Let the capacity of the system be denoted by X. Derive the probability mass function for the random variable X. (7 marks)