the number of telephone calls that arrive at a phone exchangeis often modeled as

Question

the number of telephone calls that arrive at a phone exchangeis often modeled as a poisson random variable. Assume that on theaverage there are 120 calls per hour. a) what is the prbability that there are exactly 2 calls inone hour? b) what is the prbability that there are 2 calls or less inone hour? the number of telephone calls that arrive at a phone exchangeis often modeled as a poisson random variable. Assume that on theaverage there are 120 calls per hour. a) what is the prbability that there are exactly 2 calls inone hour? b) what is the prbability that there are 2 calls or less inone hour?

Explanation / Answer

given that average telephone calls, =12 a) The probability that there are exactly 2 calls in one hourP(X = 2) = [e- 2]/ 2!                                                                                                       =e-12 (12)2 / 2                                                                                                       = 0.0004 b) The probability that there are 2 calls or less in one hour,P(X 2) = P(X=0) + P(X =1) + P(X =2)                                                                                                       =e-12 + 12 e-12 +(e-12 (12)2 / 2)                                                                                                       =0.000006144+0.00000373 + 0.0004

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