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

Question:

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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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