The random variable Y has $E[Y]= \theta$ and $\text{var}(Y)= \theta^{1.5}$. Find the transformation $W$ that makes the variance of $W$ approximately constant.

I am unsure how to approach this problem. Any help would be appreciated.


1 Answer 1


The Delta Method says that if $g$ satisfies some criteria, then $$ \text{Var}[W] = \text{Var}[g(Y)] \approx [g'(\theta)]^2\text{Var}[Y] = [g'(\theta)]^2 \theta^{1.5}. $$ So try and pick a good $g$.


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