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MaxManus
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Homework Statement
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.
Homework Equations
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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