An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hhh, then =Rhhh0. Suppose that the random variable X is defined in terms of R

as follows: =X−R2. The values of X are thus: Outcome ttt htt tht hth thh hhh tth hht

Value of

X 1 0 0 −1 −1 −2 0 −1

Calculate the probability distribution function of X, i. e. the function pXx. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.