Chapter 6, Problem 1CR

Statistical Literacy What are the requirements for a probability distribution?

To determine

To explain: The requirements for a probability distribution.

Answer to Problem 1CR

Solution: The features of the probability distribution of discrete random variable are:

1. The probability distribution consists of the description of all the possible values of the random variable.

2. The probabilities assigned to each distinct value of the random variable.

3. The sum the probabilities of all possible values of a random variable must be equal to 1.

Explanation of Solution

The assignment of probabilities to each of the possible values of a discrete random variable or to each interval of values of a continuous random variable is called as probability distribution. The probability distribution must contain all the possible values of a random variable and their assigned probabilities. The sum of these probabilities must be always equal to 1.

Probability distributions of continuous and discrete random variables are similar, except that the probability assignments are made to intervals of values in case of continuous random variable rather than to distinct values of random variable.