Consider a random variable Y with mean µ and variance σ 2 . Suppose σ 2 = Ω(µ). Consider a transformation f( ) of Y to stabilize the variance. Using the first-order Taylor series approximation, Show...

Consider a random variable Y with mean µ and variance σ². Suppose σ²
= Ω(µ). Consider a transformation f(

) of Y to stabilize the variance. Using the first-order Taylor series approximation,

Show that if f(µ) = / (1/[Ω(µ)]^½) dµ, then the variance of f(Y ) is constant, approximately.

May 13, 2022

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