Question

Let X be a random variable with the following probability distribution:

 

X

-3

6

9

P(X=x)

1/6

1/2

1/3

 

If the function of random variable is defined as f(X) = (2X+1)², find µ_g(X).

 

Answer 1

$E[(2X+1)^2]=(-3*2+1)^2*\frac{1}{6}+(6*2+1)^2*\frac{1}{2}+(9*2+1)^2*\frac{1}{3}=$

$=\frac{1254}{6}=209.$