Question

The following table shows the probability distribution for a discrete random variable.

X 13 16 18 21 23 25 26 31
P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08
The mean of the discrete random variable X is 20.59. What is the variance of X? Round your answer to the nearest hundredth.

Can anyone help me with this? Thanks.

Answer 1

\[Var(X)=E(X^2)-[E(X)]^2 \]

The mean is just \(E(X)\), which you already have. To find \(E(X^2)\):
\[ E(X^2)=\sum_{x}x^2p(x)=13^2(0.07)+16^2(0.21)+\ldots+31^2(0.08)\]