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Assume that Yi k Ynk are i.i.d. variables following a N(uk,02) distribution (k E Denote by...

Assume that Yi k Ynk are i.i.d. variables following a N(uk,02) distribution (k E Denote by Y the sample mean for sample k. { 1,2 ). a. Derive the distribution of Assume now that σ is not known and is estimated by the pooled variance S: It can be shown that en-2nx(2n -2) C. Show that S. is an unbiased estimator of the common variance σ 2 d. Show that T has a t(2n - 2) distribution.

Assume that Yi k Ynk are i.i.d. variables following a N(uk,02) distribution (k E Denote by Y the sample mean for sample k. { 1,2 ). a. Derive the distribution of Assume now that σ is not known and is estimated by the pooled variance S: It can be shown that en-2nx(2n -2) C. Show that S. is an unbiased estimator of the common variance σ 2 d. Show that T has a t(2n - 2) distribution.
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