Question

Answer asap please.

Question 2 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 ggg, then R(988) = 3. Suppose that the random variable X is defined in terms of R as follows: X=2R-2R2-4. The values of X are thus: Outcomelg bbbbbbbgebeslebx68888bbg6 Value of -4 -4 -4 -8 -8 -16 -8 -4 Calculate the probability distribution function of X, 1.e. the function Px (x). First, fill in the first row with the values of X. Then fill in the appropriate probabilities X In the second row. Value x of x 0 0 0 co 0 0 $ ?

Answer 1

In all, there are 8 possible outcomes.

We observe that in these outcomes, the possible values that X can take is -4, -8, and -16.

Now, there are 4 outcomes (gbb, bbb, bbg, bgb) that correspond to -4.

P(X = -4) = 4/8 = 1/2

Similarly,

P(X = -8) = 3/8 = 0.375

P(X = -16) = 1/8 = 0.125

X	-4	-8	-16
P(X)	0.5	0.375	0.125