The table below shows the probability distribution of X Find

The table below shows the probability distribution of X. Find V(X), that is, the variance of X to three decimal places.

Solution

E(X) = sum of x * P(X)

= -4 * 0.08 + 1 * 0.1 + 6 * 0.3 + 12 * 0.52

= 7.82

E(X^2) = sum of X^2 * P(X)

= 16 * 0.08 + 1 * 0.1 + 36 * 0.3 + 144 * 0.52

= 87.06

variance = E(X^2) - E(X)^2

= 87.06 - 7.82^2

= 25.9076