In the following probability distribution, the random variable x represents the

Question

In the following probability distribution, the random variable x represents the number of activities at least one parent of a K-5^th grade student is involved in. Draw a probability histogram. Choose the correct histogram below. Compute and interpret the mean of the random variable X. mu_x = ___ activities (Round to one decimal place as needed) Which of the following interpretation of the mean is correct? As the number of experiments decreases, the mean of the observations will approach the mean of the random variable. As the number of experiments increases, the mean of the observations will approach the mean of the random variable. The observed value of an experiment will be less than the mean of the random variable in most experiments. The observed value of an experiment will be equal to the mean of the random variable in most experiments. Compute the variance of the random variable X. sigma^2_x = ____activities^2 (Round to one decimal place as needed.) Compute the standard deviation of the random variable X. sigma_x = ____ activities (Round to one decimal place as needed.)

Explanation / Answer

a) The correct graph is Option-A)

b) Mean, E(X) = 0 * 0.088 + 1 * 0.104 + 2 * 0.325 + 3 * 0.167 + 4 * 0.316 = 2.519 = 2.5

Option-B) As the number of experiment increases, the mean of the observations will approach the mean of the random variable

c) E(X2) = 02 * 0.088 + 12 * 0.104 + 22 * 0.325 + 32 * 0.167 + 42 * 0.316 = 7.963

Var(X) = E(X) - (E(X))2 = 7.963 - 2.52 = 1.713 = 1.7

d) standard deviation = sqrt(1.7) = 1.3

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