(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume [itex] z_1, ..., z_m[/itex] are iid,[itex] z_i = μ+\epsilon_i [/itex]

[itex] \epsilon_i] [/itex]is N(0,σ^2)

Show that

f(z; μ) = g([itex] \bar{z}[/itex]; μ)h(z)

where h(·) is a function not depending on μ.

2. Relevant equations

3. The attempt at a solution

Now z is normal distributed with mean my and variance sigma^2

[itex] f(z,\mu) = \frac{1}{\sigma^2 \sqrt{2 \pi}} e^{-\frac{(z-\mu)^2}{2 \sigma^2}} [/itex]

f(z; μ) = [itex]\prod_{i=1}^m \frac{1}{\sigma^2 \sqrt{2 \pi}} e^{-\frac{(z_i-\mu)^2}{2 \sigma^2}} [/itex]

[itex] f(\bf{z},\mu) = (\frac{1}{\sigma^2 \sqrt{2 \pi}})^m \prod_{i=1}^m e^{-\frac{(z_i-\mu)^2}{2 \sigma^2}} [/itex]

but how do I go from here to

f(z; μ) = g([itex] \bar{z}[/itex]; μ)h(z)

And am I in the right track?

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# Statistics, calculate the distribution

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