# Question: The number of telephone calls arriving at an exchange during

The number of telephone calls arriving at an exchange during any given minute between noon and 1:00 P.M. on a weekday is a random variable with the following probability distribution.

X P(x)

0 .... 0.3

1 .... 0.2

2 .... 0.2

3 .... 0.1

4 .... 0.1

5 .... 0.1

a. Verify that P(x) is a probability distribution.

b. Find the cumulative distribution function of the random variable.

c. Use the cumulative distribution function to find the probability that between 12:34 and 12:35 P.M. more than two calls will arrive at the exchange.

X P(x)

0 .... 0.3

1 .... 0.2

2 .... 0.2

3 .... 0.1

4 .... 0.1

5 .... 0.1

a. Verify that P(x) is a probability distribution.

b. Find the cumulative distribution function of the random variable.

c. Use the cumulative distribution function to find the probability that between 12:34 and 12:35 P.M. more than two calls will arrive at the exchange.

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