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 heads in each outcome. For example, if the outcome is tth, then R (tth)=1.

Suppose that the random variable X is defined in terms of R as follows: X=R²3 R-2. The values of X are thus:

Outcome thh hth tth ttt hht tht hhh htt

Value of -4 -4 -4 -2 -4 -4 -2 -4

X

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.

Value _x of X

P_X^(X)