Question

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

x -1 1 8
P(X = x) 0.34 0.29 0.37

Answer 1

The distribution presented is a discrete probability distribution because each probability is between 0 and 1, and the sum of all probabilities equals exactly 1.

Step-by-step explanation:

To determine whether a given distribution is a discrete probability distribution, we must check two essential characteristics:

Each probability P(X = x) must be between 0 and 1, inclusive.

The sum of all the probabilities must equal 1.

Looking at the provided probabilities for the values of X (-1, 1, 8), the probabilities are 0.34, 0.29, and 0.37, respectively. Checking the first condition, we can see that each probability is indeed between 0 and 1. To check the second condition, we add up the probabilities:

0.34 + 0.29 + 0.37 = 1.00

Since the sum is 1, both conditions for a discrete probability distribution are satisfied. Therefore, this distribution is indeed a discrete probability distribution.