The number of telephone calls that arrive at a phone exchange is often modeled as a poisson random variable. assume that on the average there are 10 calls per hour. (a) what is the probability that there are exactly 5 calls in one hour? (b) what is the probability that there are 3 or fewer calls in one hour? (c) what is the probability that there are exactly 15 calls in two hours? (d) what is the probability that there are exactly 5 calls in 30 minutes?

Answer with Step-by-step explanation:

We know from Poisson distribution

The probability that a random process with an average arrival rate of λ occurs 'n' times in time interval of 't' is given by

Part a)

The probability for 5 calls in 1 hour is

Part b)

Probability of 3 or fewer calls occurs in 1 hour is the sum of the following probabilities

1) Only 1 call occurs in 1 hour.

2) Only 2 calls occurs in 1 hour.

3) Only 3 calls occurs in 1 hour.

4) There is no cal in 1 hour.

Thus we can write

Part c)

The probability for 15 calls in 2 hours is

Part d)

The probability for 5 calls in 30 minutes or  0.5 hours is

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step-by-step explanation:

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