How to calculate Expected value and infinity norm of a function?

How can we calculate the expected value and infinity norm of a function in Matlab?

[Torsten]

Do you mean to calculate these quantities for random variables (expected value, essential supremum) or for usual functions ? If it is for usual functions, you will have to tell us the definition of an expected value.

[Muhammad Yasir]

I am talking about random variables in particular and usual functions in general.

Consider the following case:

We select the non-linear bounded term to be a vector of scalar sigmoidal functions

applied to each coordinate of the noise vector . Where is iid Gaussian of zero mean and vriance . Where Iis identity matrix of dimension 3x3.

I am trying to simulate a similar optimization problem that is shown in the figure below:

[Muhammad Yasir]

In a book on probability theory, I have found the following definition of expected value of a random variable :

where is the average value taken by a random varibale with probaility