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.