Question: 3. The time I before a certain circuit breaker turns off the circuit and must be rest in exponentially distributed with the mean of 3

3. The time I before a certain circuit breaker turns off the circuit and must be rest in exponentially distributed with the mean of 3 hours (a) (5 pts. ) What is the probability that 5 hours pass before the circuit breaker turns off for the first time? (b) (10 pts.) Suppose a randomn variable Nis given by V = 3 + 1 Find the density function of VE 4. (10 pts ) Suppose that the independent random variables 1, and Y are both Polson with the parameters 2, and 2, respectively. Use the method of moment generating functions to find the distribution of the random variable V = 1, + 13

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