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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

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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 30E
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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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