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<math>E[X] = \frac{a+b}{2}</math> | <math>E[X] = \frac{a+b}{2}</math> | ||
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<math>E[X^2] = \frac{a^2+ab+b^2}{3}</math> | <math>E[X^2] = \frac{a^2+ab+b^2}{3}</math> | ||
Thus using the formula for variance: | Thus using the formula for variance: | ||
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| + | <math> Var(X) = E[X^2] - (E[X])^2 \!</math> | ||
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| + | One can reduce the equation to your final answer. | ||
Latest revision as of 13:17, 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.
