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the variance of a binomial random variable: | the variance of a binomial random variable: | ||
| − | + | = E[X^2] - (E[X])^2 | |
= E[X(X-1)] + E[X] - (E[X])^2 | = E[X(X-1)] + E[X] - (E[X])^2 | ||
= n*(n-1)*P^2 + n*p - (n*p)^2 | = n*(n-1)*P^2 + n*p - (n*p)^2 | ||
= n*p - n*p^2 | = n*p - n*p^2 | ||
| − | now, set n = 1000, take derivative with respect to p, set equal to zero, solve for p, and plug into var(x) equation to solve for the maximum value. | + | now, set n = 1000, take derivative with respect to p, set equal to zero, solve for p, and plug p value into var(x) equation to solve for the maximum value. |
| − | + | ||
i end up getting p = .5 so max var(X) = 250 (when X is a binomial random variable with parameter 1000) | i end up getting p = .5 so max var(X) = 250 (when X is a binomial random variable with parameter 1000) | ||
| + | |||
| + | i think this is correct but let me know if there's a mistake.. | ||
Latest revision as of 07:00, 3 November 2008
the variance of a binomial random variable:
= E[X^2] - (E[X])^2
= E[X(X-1)] + E[X] - (E[X])^2
= n*(n-1)*P^2 + n*p - (n*p)^2
= n*p - n*p^2
now, set n = 1000, take derivative with respect to p, set equal to zero, solve for p, and plug p value into var(x) equation to solve for the maximum value.
i end up getting p = .5 so max var(X) = 250 (when X is a binomial random variable with parameter 1000)
i think this is correct but let me know if there's a mistake..
