How can i calculate this

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Dec 31st 2012, 08:55 AM
Nooob

How can i calculate this

Hi guys!!!

A is white noise consisting of independent variables identically distributed Gaussian centered with variance = 1
how to calculate E(A)⁴ ???? E(.) is the Esperance
Dec 31st 2012, 10:13 AM
HallsofIvy

Re: How can i calculate this

It's not clear what you mean. By "Esperance" you mean "exected value"? Of course, then "E^4(A)" is not just that number to the fourth power. It is, rather the "4th moment", the integral of x^4 times the probability distribution, $\int_{-\infty}^\infty x^4e^{-x^2}dx$ . By symmetry, that is $2\int_0^\infty x^4e^{-x^2}dx$ .
Dec 31st 2012, 12:20 PM
Nooob

Re: How can i calculate this

thnks
Dec 31st 2012, 12:24 PM
ILikeSerena

Re: How can i calculate this

For a standard normal distribution X, we have:

$E(X^4) = {1 \over \sqrt{2\pi}}\int_{-\infty}^\infty x^4 e^{-\frac 1 2 x^2}dx = 3$

as you can see here: Wolfram|Alpha Results

Note that the standard normal distribution has probability density ${1 \over \sqrt{2\pi}}e^{-\frac 1 2 x^2}$ .

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