Chapter 6, Problem 1CQ

Explain why the following is not a probability distribution.

To determine

To explain whether the given distribution is probability distribution.

Answer to Problem 1CQ

This is not a probability distribution as the sum of probabilities are not equal to 1.

Explanation of Solution

Given:

x	6	7	8	9	10
P(x)	0.32	0.11	0.19	0.28	0.03

A distribution is considered as a valid probability distribution when sum of all the probability of all outcomes of an experiment is equal to 1.

Let’s check whether the sum of probability is one or not:

  $\begin{array}{l}=P\left(6\right)+P\left(7\right)+P\left(8\right)+P\left(9\right)+P\left(10\right)\\ =0.32+0.11+0.19+0.28+0.03\\ =0.93\end{array}$

Since the sum of all probabilities is not equal to 1, therefore, it is not a probability distribution.