Let X1, ...,Xn and Y1, ...,Ym be two random samples from distributions with means 1 and 2, respectively, and the same variance 2. (i) Find

Let X1, ...,Xn and Y1, ...,Ym be two random samples from distributions with means μ1 and μ2, respectively, and the same variance σ2. (i) Find E(X − Y ) and Var(X − Y ). (ii) Assuming that μ1 = μ2 and both samples are of equal size, find n = m such that P(|X − Y | > σ/4) ≤ 0.05.