(Answered) A machine is subject to shocks arriving from two

Statistics

A machine is subject to shocks arriving from two independent sources. The shocks from source 1 arrive according to a Poisson Process (PP) with rate 3 per day and those from source 2 at rate 4 per day, also forming a Poisson Process.

(a) What are the mean and variance of the total number of shocks from both the sources over an 8-hour shift.

(b) What is the probability that the rst incoming shock is from source 1?

(d) Assume that we have received a total of 5 shocks in 2 hours. What is the probability that there are exactly 2 shocks from source 1?

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