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revised $\mathbb E[\frac{\partial}{\partial\theta}\log f(X;\theta)]^2$ and $\mathbb E[\frac{\partial^2}{\partial\theta^2}\log f(X;\theta)]$
Added note for when $n = 1$, clearly $C(1)$ is not equal to 0.
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comment 3 random numbers to describe point on a sphere
The link here: math.stackexchange.com/questions/44689/… , may be informative for your application.
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comment How Do I Get This Joint Density Function?
I think there is a deterministic relationship between $X$ and $Y$. Therefore, the joint distribution of $X$ and $Y$ will take non-zero values along the indices which map to and fro each other, and will take zero values otherwise.
Jul
28
comment Conditional Probability, Lack of Dependence on a Parameter
The way I see it is: If the conditional distribution of $Z$ given $X$ and $Y$ is the same as the conditional distribution of $Z$ which depends only on $Y$, then $X$, $Y$, $Z$ form a Markov chain in that order. If $p(Z\mid X,Y) = p(Z\mid Y)$, then the Markov chain is formed. If $Z = f(Y)$ and $Y$ is known, then our characterization of $f(Y)$ knowing the additional information $X$ is the same as the characterization not knowing $X$ since $Z$ is a deterministic function of only the random variable $Y$.
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accepted Conditional Probability, Lack of Dependence on a Parameter
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