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

 

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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. 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.

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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 ... View the full answer