If Y is a random variable and c is a positive constant, then the standard deviation of
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If Y is a random variable and c is a positive constant, then the standard deviation of the probability distribution of cY equals cσ(Y ). Suppose Y is a binomial variate and let πˆ = Y /n.
a. Based on the binomial standard deviation for Y , show that σ(ˆπ) = π(1 − π)/n.
b. Explain why it is easier to estimate π precisely when it is near 0 or 1 than when it is near 0.50.
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