Question

Statistics

Answer 1

i more or less have the result for part A, but part B seems like there has to be some kind of identity that i'm overlooking.
For part A i used the identity that \[\sum_{i=1}^{n}(X_{i}-Xbar)(Xbar-\mu) = (Xbar-\mu)\sum_{i=1}^{n}(X_{i}-Xbar) = 0\]
correct me if that's wrong to use.

Answer 2

that is part of what you need to do.

What part of (B) are you stuck on

Answer 3

so after applying the product of the sequence to the normal distribution i get\[\prod_{i=1}^{n}\frac{\exp(\frac{ x _{i}- \mu)^2 }{ \sigma^2 }) }{ \sigma (2 \pi )^\frac{ 1 }{ 2 } }\]i then get that this is equivalent to\[\frac{ 1 }{ \sigma^n(2\pi)^\frac{ n }{ 2 } }\exp(\frac{ \sum_{i=1}^{n}(x _{i}-\mu)^2 }{ 2\sigma^2 })\]if a sufficient statistic is defined as\[f _{n}(x|\theta)=u(x)v[r(x),\theta]\]does that mean that i set everything in my exponential as my V, and the constant in front as my U, and because V is a function of the statistic and the unknown parameter, in my case being\[\sigma^2\]that i have then proved it's sufficient? I may or may not be making a huge mistake, it's just so complicated