Question: Let X11, X12, . . . , X1n1 be a random sample with sample mean X1 from a normal population with mean 1 and variance

Let X11, X12, . . . , X1n1 be a random sample with sample mean X1 from a normal population with mean μ1 and variance σ12 , and let X21, X22, . . . , X2n2 be a random sample with sample mean X-bar2 from a normal population with mean μ2 and variance σ22 . Assume the two samples are independent. Show that the sampling of X-bar1 – X-bar2) is normal with mean μ1 – μ2 and variance σ12 / n1 + σ22 / n2.

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