How to get the mean of a function when the input of the function is a distribution?

I want to get the expectation of y=sin(x) when x follows a distribution described below. But the second line has error. How can I fix this?

    x=makedist('Uniform','Lower',0,'Upper',pi/2)
    y=sin(x);
    mean(y)

Answer 1

[Walter Roberson]

The easiest approach is the numeric one:

>> mean(sin(random(x,1,10000)))
ans =
         0.636616269663442
>> mean(sin(random(x,1,10000)))
ans =
         0.636757666186139
>> mean(sin(random(x,1,10000)))
ans =
         0.632276664694085

If you need the theoretical answer then rely upon the fact that you have a uniform distribution and calculate the expectation of sin(x) x from 0 to pi/2 symbolically:

syms x
int(sin(x),x,0,pi/2)/(pi/2)

Numerically this comes out as about 0.636619772367581

Answer 2

[Torsten]

I think you will have to go back to the general definition of the mean of a probability distribution.

Best wishes

Torsten.