How to calculate the mathematical expectation of a function?

Question

Suppose that $T$ is a random variable, $F(T)$ the function of random variables. How can I compute the expectation of a function of random variables if the probability density function (PDF) $g(t)$ for $T$ is given?

https://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician — 311411, Jan 20 '22 at 13:48

score 0 · Answer 1 · edited Jan 20 '22 at 13:52

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For instance, suppose $T\sim g(t),\;\,$ $\bar{T}=\int_{0}^{\infty}t \cdot g(t)dt$, and $f(t)= T^2$.

How to compute the $E[f(t)]$?

Answer: $\;\;E[{f(t)}]=\int_{0}^{\infty}f(t)g(t)dt$

edited Jan 20 '22 at 13:52

311411

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answered Jan 20 '22 at 13:45

Yang

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No : see the answer of Did here – Jean Marie Jan 20 '22 at 15:20

How to calculate the mathematical expectation of a function?

1 Answers1