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 Sy/Vm assuming of = o (X – Y) – (141 – H2) (c) - (X -Y) – (41 – 42) (d) where S2 is the pooled variance (# + #) sA

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Need help on this one, and how to prove the following distribution after determining the distribution for each. 

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
Sy/Vm
assuming of = o
(X – Y) – (141 – H2)
-
(c)
V +
(X – Y) – (41 – H2)
m
(d)
where S2 is the pooled variance
(4 + #) sA
Transcribed Image Text: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 Sy/Vm assuming of = o (X – Y) – (141 – H2) - (c) V + (X – Y) – (41 – H2) m (d) where S2 is the pooled variance (4 + #) sA
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