X1 and S2 1 are the sample mean and sample variance from a population with mean and variance similarly, and are the sample mean and sample variance from a second independent population with mean 1 and variance 2 2 The sample sizes are n1 and n2, respectively (a) Show that X1 X2 is an unbiased estimator of (b) Find the standard error of X1 X2 How could you estimate the standard error

Question: X1 and S2/1 are the sample mean and sample variance from a population with mean and variance similarly, and are the sample mean and sample

X1 and S2/1 are the sample mean and sample variance from a population with mean μ and variance similarly, and are the sample mean and sample variance from a second independent population with mean μ1 and variance σ2/2. The sample sizes are n1 and n2, respectively.
(a) Show that X1 – X2 is an unbiased estimator of μ.
(b) Find the standard error of X1 – X2. How could you estimate the standard error?

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