(New page: To find the maximum variance of a Bernoulli RV first find the variance equation.) |
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To find the maximum variance of a Bernoulli RV first find the variance equation. | To find the maximum variance of a Bernoulli RV first find the variance equation. | ||
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| + | <math> Var(X) = E[X^2] - (E[X])^2 \!</math> | ||
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| + | We know that for Bernoulli RVs | ||
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| + | <math> E[X^2] = p \!</math> | ||
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| + | <math> E[X] = p \!</math> | ||
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| + | Plug these values into the variance equation, differentiate with respect to p, set equal to 0 and find the value of p that results in the largest value for the variance. | ||
Latest revision as of 12:16, 2 November 2008
To find the maximum variance of a Bernoulli RV first find the variance equation.
$ Var(X) = E[X^2] - (E[X])^2 \! $
We know that for Bernoulli RVs
$ E[X^2] = p \! $
$ E[X] = p \! $
Plug these values into the variance equation, differentiate with respect to p, set equal to 0 and find the value of p that results in the largest value for the variance.
