Suppose Yi is distributed i.i.d. N(0,sigma^2) for i=1,2,...,n. a.) Show that E(Yi^2/sigma^2)=1 b.) show that W=(1/sigma^2)Sum(Yi^2) is
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Suppose Yi is distributed i.i.d. N(0,sigma^2) for i=1,2,...,n.
a.) Show that E(Yi^2/sigma^2)=1
b.) show that W=(1/sigma^2)Sum(Yi^2) is distributed chi^2
c.) Show that E(W)=n [Hint: Use your answer to (a).]
d.)Show that V=Y1/(Sqrt((Sum Yi^2)/(n-1)) is distributed t(subscript n-1).
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