Let X be a random sample of size n from N(41, o?) and let Y be a random sample of size m from N(42,03) where X and Y are independent. Determine the distribution of each of the following: Y - 42 (a) Sy/Vm (b) assuming of = o3 (X – Y) – (41 – 2) (c) (X-Y)- (41 – H2) (d) where S is the pooled variance (# + #) %s/

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