An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of heads (h) and...

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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 heads in each outcome. For example, if the outcome is hht, then N (hht) = 2. Suppose that the random variable X is defined in terms of N as follows: X=6N-2N -2. The values of X are given in the table below. Outcome hht ttt tth hth htt hhh thh tht Value of X 2 -2 2 2 2 -2 2 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) 0 0 7 010 X HE 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 heads in each outcome. For example, if the outcome is hht, then N (hht) = 2. Suppose that the random variable X is defined in terms of N as follows: X=6N-2N -2. The values of X are given in the table below. Outcome hht ttt tth hth htt hhh thh tht Value of X 2 -2 2 2 2 -2 2 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) 0 0 7 010 X HE