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.

Expert Solution

orchestra answered 1 year ago

Problem 1 Let X1, X2, . . . , Xn be independent Uniform(0,1) random variables. (...

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2. Let X1, X2, . . . , Xn be independent, uniformly distributed random variables on...

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Let X1, … , Xn be independent where Xi is normally distributed with unknown mean µ...

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

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