Taylor expansions for the moments of functions of random variables

In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite. This technique is often used by statisticians.
First moment
Noting that E[X − μ_{X}] = 0, the 2nd term disappears. Also E[(X − μ_{X})^{2}] is . Therefore,
where μ_{X} and are the mean and variance of X respectively.
It is possible to generalize this to functions of more than one variable using multivariate Taylor expansions. For example,
Second moment
Analogously,
This is a special case of the delta method. For example,
See also
Categories: Statistical approximations
 Algebra of random variables
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