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
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, . By symmetry, that is .
For a standard normal distribution X, we have:
as you can see here: Wolfram|Alpha Results
Note that the standard normal distribution has probability density .