Question

show that x(bar ) is a sufficient estimator of the population mean of normal population with known population variance .

Answer 1

@Valpey ps help

Answer 2

@Zarkon pls help

Answer 3

factorization theorem.

Answer 4

what do we factorize ,the mgf or the main function?

Answer 5

the joint distribution of \(X_1,X_2,\ldots,X_n\)
where the \(X_i\) are independent normal(\(\mu,\sigma^2\)) random variables

Answer 6

does it mean that i must find the maximum likelihood function for normal first?

Answer 7

the joint distribution is just the product of the individual distributions since you have independence. (the likelihood function)

Answer 8

do you mean the product of MGF?

Answer 9

i realy don't understand this question can u pls show me atleast 3 steps