Question 11677
 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