We have to find E(X) first:

MATH

Then:
MATH

Checking this using the other formula:

V(X) = E(X 2) − [E(X)]2

For this, we need to work out the expected value of the squares of the random variable X.

X 8 12 16 20 24
X2 64 144 256 400 576
P(X) $\dfrac{1}{8}$ $\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{4}$ $\dfrac{1}{12}$



MATH

We found E(X) before: E(X) = 16

V(X) = E(X2) − [E(X)]2 = 276 - 162 = 20, as before.