Suppose that X, X2,…, Xn are iid random variables with a common mean and common variance o2. Let X…

Suppose that X, X2,…, Xn are iid random variables with a common mean and common variance o2. Let X…

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Suppose that X₁, X2,…, Xn are iid random variables with a common
mean and common variance o2. Let
X
i=1
n
Xi
(a) Show that the sample mean X is an unbiased estimator for μ.
(b) Find the variance of X.
(c) Explain how the iid assumption is important in calculating the mean
and variance for X.

Expert Answer:

Answer rating: 100% (QA)

a To show that the sample mean X is an unbiased estimator for we need to show that the expected value of X is equal to The sample mean X is calculated
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