Referring to Exercise 7.9, use a die to generate samples of size 3. Investigate the sampling distribution of the number of times a value 1 occurs in a sample of size 3.
(a) Roll the die and assign X = 1 if 1 dot shows and X = 0, otherwise. Repeat until you obtain a total of 25 samples of size 3. Calculate the relative frequencies, among the 75 values, of 1. Compare with the population probabilities and explain why they should be close.
(b) Let a random variable V equal 1 if at least one value of X in the sample is 1. Set V equal to 0 otherwise. Then the relative frequency of [7 = 1] is an estimate of P[Y = I], the probability of at least one value 1 in the sample of size 3. Give your estimate.