##### Question

In: Statistics and Probability

# Determine whether the distribution is a discrete probability distribution. If not, state why.

Determine whether the distribution is a discrete probability distribution. If not, state why.

 x P(x) 0 0.1 1 0.5 2 0.05 3 0.25 4 0.1

## Solution

##### Step #1

Given distribution is in table form.

 x 0 1 2 3 4 P(x) 0.1 0.5 0.05 0.25 0.1

Check whether the distribution is a discrete probability distribution.

To be a discrete probability distribution, we must have a numerical random variable $$x$$ such that $$P(x)$$ must satisfy the preceding three requirements.

1. The variable $$x$$ is a discrete random variable and its values are associated with probabilities.

2. $$\sum P(x)=P(0)+P(1)+P(2)+P(3)+P(4)$$

$$=0.1+0.5+0.05+0.25+0.1$$

$$=1$$

3. Each value of $$P(x)$$ is between 0 and 1 .

The given table is a discrete probability distribution because it satisfies the discrete probability distribution's three requirements.