Suppose that the genders of the three children of a certain family are soon to b

Question

Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" () and "boys" (), which we write , , etc. For each outcome, let be the random variable counting the number of girls in each outcome. For example, if the outcome is , then . Suppose that the random variable is defined in terms of as follows: . The values of are thus: Outcome Value of
Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of . Then fill in the appropriate probabilities in the second row. value x of X Px (X)

Explanation / Answer

As you can see, there are 8 possibilities.

For x = -2, it occurred once.

For x = -1, it occurred 3 times.

For x = 0, 3 times.

For = 1, once.

Thus,

x -2 -1 0 1
P(x)   1/8   3/8   3/8   1/8 [ANSWER]

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