The arrivals of new telephone calls at a telephone switching office is a Poisson

Question

The arrivals of new telephone calls at a telephone switching office is a Poisson process M) with an arrival rate of =4 calls per second. An experiment consists of monitoring the switching office and recording Mt) over a 10-second interval. (a) What is Pstu 0), the probability of no phone calls in the first second of b) What is PU 4), the probability of exactly four calls arriving in the first second of (c) What is P2), the probability of exactly two calls arriving in the first two observation? observation? seconds?

Explanation / Answer

POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.   
x = is the number of independent trials
I.
mean =
= 4
a.
P( X = 0 ) = e ^-4 * 4^0 / 0! = 0.01832
b.
P( X = 4 ) = e ^-4 * 4^4 / 4! = 0.19537
c.
for 2 second the mea rate is 8
P( X = 2 ) = e ^-8 * 8^2 / 2! = 0.01073

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