Question

Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not.

x −3 1 5

P(X=x) 1/2 1/8 3/8

First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision.

Decide yes or no and why

Answer 1

The given distribution is a discrete probability distribution, as each individual probability is between zero and one, and the total probability sums to one.

Step-by-step explanation:

The distribution given is a discrete probability distribution if it satisfies two essential criteria: first, each probability P(X=x) must be between zero and one, inclusive, and second, the sum of all probabilities must equal one.

For the values provided, x = -3, 1, 5, and the corresponding probabilities are P(X=-3) = 1/2, P(X=1) = 1/8, P(X=5) = 3/8.

To determine if this is a discrete probability distribution, we add the probabilities: 1/2 + 1/8 + 3/8 = 4/8 + 1/8 + 3/8 = 8/8 = 1. Additionally, each probability is between zero and one.

Thus, the distribution given is indeed a discrete probability distribution.