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(Answered)-Problem 1) In a communication system with binary input X and

**Problem 1) In a communication system with binary input X and binary output Y, the transmitted signal**?X**?0,1**?**with probability P(X=0)**?**and P(X=1) = 1-p.**?**The transmission channel can be modeled by the following conditional probability: P(Y=0 | X = 1) = q**?**and P(Y=1|X=0) = r.**?**Find the probability P(Y=0)****and simplify the result if q=r .**

**Problem 2)**?**The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.**

**a. What is the probability that there will be exactly 3 power outages in a year?**

**b. What is the probability that there will be at least 3 power outages in a year?**

**c. What is the probability that the number of outages is between 1 and 3 (1 and 3 inclusive)?**

**Please include the steps involved with formulas and how the decision was arrived in clear steps about do it.**

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DATE ANSWEREDOct 07, 2020

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