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

Form the given table we can see that X can take three values -3, 5, and -1. Total number of outcomes are 8. Out of these 8 outcomes three are -3. So

P(X=-3) = 3/8

And out of these 8 outcomes one is 5. So

P(X=5) = 1/8

And out of these 8 outcomes four are -1. So

P(X=-1) = 4/8

Following is the completed table:

X -3 -1 5 P(X) (3/8) (4/8) (1/8)

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