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

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Muhammad Yasir 2021-7-18

评论： Muhammad Yasir 2021-7-26

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

Muhammad Yasir 2021-7-20

编辑：Muhammad Yasir 2021-7-20

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 2021-7-26

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

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