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# AnswerGiven,The aivals of phone calls at a telephone switching office is a Poisson random process N(t) with all artival rate 1 4 calls per second. We monitor N(t) s...

## Question

###### AnswerGiven,The aivals of phone calls at a telephone switching office is a Poisson random process N(t) with all artival rate 1 4 calls per second. We monitor N(t) starting from t = 0 over a 10-second interval. Let Sn be the time of the airival of the nt call_What is P(N(1) =0) , the probability of no phone calls during the first second? Here, Iam denoting lambda by L in the below discussion for my convenience Poisson distribution;, P(r) = (e^L )* (L^VL! above P(r) signifies the probability of &q

Answer Given, The aivals of phone calls at a telephone switching office is a Poisson random process N(t) with all artival rate 1 4 calls per second. We monitor N(t) starting from t = 0 over a 10-second interval. Let Sn be the time of the airival of the nt call_ What is P(N(1) =0) , the probability of no phone calls during the first second? Here, Iam denoting lambda by L in the below discussion for my convenience Poisson distribution;, P(r) = (e^L )* (L^VL! above P(r) signifies the probability of "time between two successive calls i31" So, for 1 = 0 P(0) = e^-4 2 What is P(N(4)-N(3) = 4), the probability of four phone calls arrive between the third and the fourth second Here, It is nothing but P(4) P(4) = (32/3) *e^-4

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