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Question

Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus

triples of "girls" (g

) and "boys" (b

), which we write gbg

bbb

, etc. For each outcome, let R

 be the random variable counting the number of girls in each outcome. For example, if the outcome is gbb

, then =

R

gbb

1

. Suppose that the random variable X

 is defined in terms of R

 as follows: =

X

2

R

2

2

R

3

. The values of X

 are thus:Outcomebgg

ggb

bbb

ggg

bbg

gbb

gbg

bgb

Value of

X

1

1

3

9

3

3

1

3

Calculate the probability distribution function of X

, i.e. the function p

X

x

. First, fill in the first row with the values of X

. Then fill in the appropriate probabilities in the second row. 

Value

x

of

X

4

3

6

P

X

x

5

2

8

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