(Created page with "=Proof that <math>I(θ) = E[(s(θ;X))^2]</math>= Recall that: <div style="margin-left: 3em;"> <math> \begin{align} \bar Var(Y) &= E[(Y-E(Y))^2]\\ &= \int_a^b g(x) dx \\ &= \fr...") |
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\begin{align} | \begin{align} | ||
\bar Var(Y) &= E[(Y-E(Y))^2]\\ | \bar Var(Y) &= E[(Y-E(Y))^2]\\ | ||
| − | &= | + | &= E[Y^2-2YE[Y]+(E[Y])^2]\\ |
&= \frac{\mu_0}{2 \pi a \cdot b} | &= \frac{\mu_0}{2 \pi a \cdot b} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
</div> | </div> | ||
Revision as of 21:55, 6 December 2020
Proof that $ I(θ) = E[(s(θ;X))^2] $
Recall that:
$ \begin{align} \bar Var(Y) &= E[(Y-E(Y))^2]\\ &= E[Y^2-2YE[Y]+(E[Y])^2]\\ &= \frac{\mu_0}{2 \pi a \cdot b} \end{align} $
