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    Probability distribution function

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    Please see the attached file for full problem description with all proper "X" symbols.

    Can you show me how to complete this kind of problem? 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 boys 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 bbg bgg gbb bbb gbg ggb bgb ggg

    Value of X -6 -6 -6 -4 -6 -6 -6 -4

    Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of , in increasing order. Then fill in the appropriate probabilities in the second row. Enter each probability as an exact fraction.

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