An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads"(h) and "tails"(t) which we write ttt ,hth, etc. For each outcome, let be the random variable counting the number of tails in each outcome. For example, if the outcome is hhh, then R(hhh)= 1. Suppose that the random variable X is defined in terms of R as follows: X =R - 1

The values of are thus:
Outcome htt tht tth hhh hht hth ttt thh
Value of X -5 5 -5 -3 -3 -3 -9 -3

a. Calculate the probability distribution function of X, i.e. the function P_X(X). First, fill in the first row with the values of X, then fill in the appropriate probabilities in the second row.