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.
XP(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.