Question 11677: The random variable x represents the number of boys in a family of three children. Asuming tha boys and girls are likely, find mean and standard deviation for the random variable x.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! There were some errors in my previus solution.
Note X has 4 possible outcomes, namely 0,1,2 or 3.
Pr(X= 0) = Pr(X=3) =(1/2)^3 =1/8, and
Pr(X= 1) = Pr(X=2) = 3*(1/2)^3 =3/8
Mean = E(X) = 0* Pr(X= 0)+ 1* Pr(X= 1) + 2* Pr(X= 2)+ 3* Pr(X= 3)
= 3/8 + 2*3/8 +3/8 = 12/8 = 1.5
Let var be the variance ,and sd =sqrt(var) be the standard deviation.
Use the formula var = E(X^2) – E(X)^2.
Since E(X^2) = 0* Pr(X= 0)+ 1* Pr(X= 1) + 2^2* Pr(X= 2)+ 3^2* Pr(X= 3)
= 3/8 + 4*3/8 +9/8 = 24/8 = 3.
We get var = 3 – (1.5)^2 = 0.75, and so
sd of X = sqrt(0.75) = 0.866
Kenny
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