An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt

Question

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 hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X= 2N-2N^2-2. The values of X are given in the table below.

Outcome        ttt     hht    thh     tht    tth    hhh    htt     hth
Value of X    -14     - 2    - 2      -6     -6     -2      -6       -2
Calculate the probabilities P(X=x) of the probability distribution of 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)             ______      _______     ______

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