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 readom variable counting the number of heads in each outcome. For example, if the outocme id tht, the R(tht)=1. Suppose that the reandom variable X is defined in terms of R as follows: X = 4R - 2R^2 - 1. The values of X are thus:
| Outcome |
hth |
htt |
thh |
ttt |
hht |
tht |
tth |
hhh |
| Value of x |
-1 |
1 |
-1 |
-1 |
-1 |
1 |
1 |
-7 |
Compute the probability distribution function of X, i.e. the function Px (x).