A communication system has 3 links. Link #1 is connected in parallel with link #2. These...

 

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A communication system has 3 links. Link #1 is connected in parallel with link #2. These two links are connected in series with link #3. Each link may fail or not fail independently of the other links in a given interval of time. Define the events F (Component #i fails), i = 1,2,3 Assume that P{F} = 0.2. (a) Determine the probability of success of the communication system. (b) Let M. denote the capacity of link #i in megabits per second. Assume that M = 10, M25 and Ms = 5. Let the capacity of the system be denoted by X. Determine the expected value of X given that the communication link is functioning properly. (c) Determine the probability that link #1 is the only link functioning given that the communication system is not functioning properly. A communication system has 3 links. Link #1 is connected in parallel with link #2. These two links are connected in series with link #3. Each link may fail or not fail independently of the other links in a given interval of time. Define the events F (Component #i fails), i = 1,2,3 Assume that P{F} = 0.2. (a) Determine the probability of success of the communication system. (b) Let M. denote the capacity of link #i in megabits per second. Assume that M = 10, M25 and Ms = 5. Let the capacity of the system be denoted by X. Determine the expected value of X given that the communication link is functioning properly. (c) Determine the probability that link #1 is the only link functioning given that the communication system is not functioning properly.