X₁, X₂.... Xn be a random sample of size n from a normal distribution given a mean nd standard deviation o. Let Y₁, Y₂,.. Ym be an independent random sample of size m a normal distribution with mean µy and the same standard deviation o. Let S and S e the two corresponding sample variances, and S be the pooled variance given by (n − 1)S² + (m − 1)S} _ Σï-1(X; − X)² + Σ²²₁(Y; − Ỹ)² - S² = n+m-2 n+m-2 Then find the distribution of X − Y - (lx − ly) T = 1 1 =+ P√n m

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