Question: If X1, X2, . . . , Xn are independent random variables having identical Bernoulli distributions with the parameter , then is the proportion

If X1, X2, . . . , Xn are independent random variables having identical Bernoulli distributions with the parameter θ, then is the proportion of successes in n trials, which we denote by Θ. Verify that
(a) E(Θ) = θ;
(b) var(Θ) = θ(1 – θ)/n .

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