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(Solved): (a) What are the distributions of: (i) (x_(i))/(\sigma \sqrt(i)); (ii) (x_(i)^(2))/(\sigma ^(2)i); a ...
(a) What are the distributions of: (i)
(x_(i))/(\sigma \sqrt(i)); (ii)
(x_(i)^(2))/(\sigma ^(2)i); and (iii)
\sum_(i=1)^n (x_(i)^(2))/(\sigma ^(2)i). (b) Prove or disprove that the expression of the asymptotic confidence interval
(nlongrightarrow\infty )for
\sigma ^(2)is
widehat(\sigma )^(2)(1+-1.96\sqrt((2)/(n)))where
widehat(\sigma )^(2)is the maximum likelihood estimate of
\sigma ^(2)found in Question 1 (d)
