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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
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.
-
d) Find the
expected value of the random variable in the problem. -
e) Also find the variance of the random variable and its standard deviation.
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