Question

explain how to find the mean of a discrete random variable. choose the correct answer below. a. to find the mean of a random variable, add the possible values of the random variable and divide by the number of possible values. b. to find the mean of a random variable, add the probabilities of each value and divide by the number of possible values. c. to find the mean of a random variable, find the weighted average of the squared deviations, using the probabilities as weights. d. to find the mean of a random variable, multiply each value of the random variable by its probability and then add those products.

Explanation:

The mean (expected value) of a discrete random variable \(X\) is calculated by multiplying each possible value \(x_i\) of the random variable by its corresponding probability \(P(x_i)\) and then summing up these products. Mathematically, \(E(X)=\sum_{i}x_iP(x_i)\). This is a weighted - average concept where the probabilities are the weights. Option A describes the arithmetic mean of non - probabilistic values, option B is incorrect as adding probabilities and dividing by number of values is not how mean of a random variable is found, and option C describes the calculation of variance.

Answer:

D. To find the mean of a random variable, multiply each value of the random variable by its probability and then add those products.