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in class we found the following: | in class we found the following: | ||
| − | <math>E[ | + | <math>E[X] = \frac{a+b}{2}</math> |
| + | |||
| + | <math>E[X^2] = \frac{a^2+ab+b^2}{3}</math> | ||
| + | |||
| + | Thus using the formula for variance: | ||
| + | |||
| + | <math> Var(X) = E[X^2] - (E[X])^2 \!</math> | ||
| + | |||
| + | One can reduce the equation to your final answer. | ||
Latest revision as of 12:17, 2 November 2008
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.
