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 R9gbb)=1. Suppose that the random variable X is defined in terms of R as follows: X=2R^2-4R-2. The values of X are thus:

Complete Question

The complete question is shown on the first uploaded image

  Value  x of X     -3    -7     -15

Step-by-step explanation:

From the question we are told that  

     The values of X are  

     The total number of outcomes is  n =  8

The probability distribution function of X is evaluated as follow

Where   is the number of time  X = -3  occurred and from the table the value is  

     Therefore

Now  

Where from table  

So  

Also