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 N be the random variable counting the number of tails in each outcome. For example, if the outcome is htt, then N (htt) = 2. Suppose that the random variable X is defined in terms of N as follows: X= 2N-2. The values of X are given in the table below.

Outcome htt hhh tth hht thh ttt hth tht

Value of X 2 2 2 0 0 4 0 2

calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with values of X. then fill in the appropriate probabilities in the second row.