i. If u is known and o? is unknown, show that (X,-p)² is a sufficient i=1 statistic for o². Show all steps of your working. and o? are both unknown, show that X (i.e. the sample mean) and S (i.e. the sample variance) are jointly sufficient for u and o². ii. If

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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1. (a) Let X
{X1, X2, , Xn} be a random sample from a normal distribution
....
with mcan u and variance o.
i. If u is known and o? is unknown, show that (X, -p)² is a sufficient
i=1
statistic for o². Show all steps of your working.
ii. If u and o2 are both unknown, show that X (i.e. the sample mean) and
S (i.e. the sample variance) are jointly sufficient for u and o?.
Transcribed Image Text:1. (a) Let X {X1, X2, , Xn} be a random sample from a normal distribution .... with mcan u and variance o. i. If u is known and o? is unknown, show that (X, -p)² is a sufficient i=1 statistic for o². Show all steps of your working. ii. If u and o2 are both unknown, show that X (i.e. the sample mean) and S (i.e. the sample variance) are jointly sufficient for u and o?.
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