SOLUTION: Find the variance of a random variable X having the following probability distribution. The random variable X has expected value E(x) = .8. x P(X = x) -4 - 0.3 0 - 0.2 4 - 0

Algebra ->  Probability-and-statistics -> SOLUTION: Find the variance of a random variable X having the following probability distribution. The random variable X has expected value E(x) = .8. x P(X = x) -4 - 0.3 0 - 0.2 4 - 0      Log On


   

Question 604855: Find the variance of a random variable X having the following probability distribution. The
random variable X has expected value E(x) = .8.
x P(X = x)
-4 - 0.3
0 - 0.2
4 - 0.5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Variance

sigma^2 = Sum( P(X = xi) * (xi - E(X) )^2 )

sigma^2 = [0.3*(-4 - 0.8)^2] + [0.2*(0 - 0.8)^2] + [0.5*(4 - 0.8)^2]

sigma^2 = [0.3*(-4.8)^2] + [0.2*(-0.8)^2] + [0.5*(3.2)^2]

sigma^2 = 0.3*23.04 + 0.2*0.64 + 0.5*10.24

sigma^2 = 6.912 + 0.128 + 5.12

sigma^2 = 12.16

So the variance is 12.16