The probability distribution of X, the number of customers in line (including the one being served, if any) at a checkout counter in a department store, is given by P(X = 0) = 0.25, P(X = 1) = 0.25, P(X = 2) = 0.20, P(X = 3) = 0.20, and P(X = 4) = 0.10.
a. Use simulation to generate 500 values of this random variable X.
b. Is the simulated distribution indicative of the given probability distribution? Explain why or why not.
c. Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution?
d. Repeat parts a through c with 5000 simulated values rather than 500. Explain any differences you observe.