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.