The problem only asks for the variance of a uniform R.V. on the interval [a,b]

in class we found the following:

$ E[X] = \frac{a+b}{2} $

$ E[X^2] = \frac{a^2+ab+b^2}{3} $

Thus using the formula for variance:

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

One can reduce the equation to your final answer.

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood