Consider the illustrative experiment introduced in Example 3.1 in Chapter 3, and in Example 4.1 of Chapter 4, which involved tossing a coin 3 times and recording the number of observed tails. For a spe- ci?c coin, after performing this three-coin toss experiment exactly 10 times under identical conditions, the following result set was obtained:
S1 = {0, 1, 3, 2, 2, 1, 0, 1, 2, 2}.
(1) What is the random variable X, and for a generic coin, what is the theoretical ensemble description f (x)? (2) How is the speci?c experimental result related to the random variable, X? (3) For a speci?c coin for which p = 0.5 compute the probabilities of obtaining 0, 1, 2 or 3 tails in each experiment. How consistent with the observed results are the theoretical probabilities?