Look at the first value of : = 0, and look at the table listing all the possible samples. Since the only outcome with this value is TTT and has probability 1/64, this is the probability that = 0.
Now look at the second value: = 1/3. There are three outcomes with this value: HTT, THT, and TTH. Since each of them has probability 3/64, the probability that one of them occurs is 3/64 + 3/64 + 3/64 = 9/64.
Continue in this manner to obtain the probabilities for all the values of .
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