Chapter 5.1, Problem 1E

To determine

The given table represents a valid discrete probability distribution or not.

Answer to Problem 1E

Solution:

The given distribution is a valid discrete probability distribution.

Explanation of Solution

Given:

The distribution is given as,

$x$	$P\left(X=x\right)$
1	0.2
2	0.6
3	0.05
4	0.15
5	0.0

Steps:

The conditions required to check the valid discrete probability distribution are,

(i) The sum of all the probabilities is 1.

(ii) The individual probability should be between 0 and 1.

Now, the sum of all probabilities is,

$\begin{array}{rll}P\left(X\right)& =& 0.2+0.6+0.05+0.15+0.0\\ & =& 1.0\end{array}$

This shows that sum of all the probabilities is 1.

Also, it can be observed that the individual probability is between 0 and 1.

Therefore, it satisfies both the conditions and thus, the given distribution is a valid discrete probability distribution.