Find the expected value of the random variable in given problem. Also find the variance of the random variable and its standard deviation.
Problem
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.