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...

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 hhh, then =Rhhh3. Suppose that the random variable X is defined in terms of R as follows: =X−2R2−4R3. The values of X are given in the table below.

Calculate the values of the probability distribution function of X, i.e. the function pX. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.