Let X1,...,Xn be independent random variables,and let X=X1+...+Xn be their sum. 1. Suppose that each Xi...

Let X₁,...,X_n be independent random variables,and let X=X₁+...+X_n be their sum.

1. Suppose that each X_i is geometric with respective parameter p_i. It is known that the mean of X is equal to μ, where μ > 0. Show that the variance of X is minimized if the p_i's are all equal to n/μ.

2. Suppose that each X_i is Bernoulli with respective parameter p_i. It is known that the mean of X is equal to μ, where μ > 0. Show that the variance of X is maximized if the p_i's are all equal to μ/n.

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orchestra answered 1 year ago

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