Suppose that the genders of the three children of a certain

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)

Solution

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: