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

Question

Jen W 2018-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/377134-how-to-get-the-mean-of-a-function-when-the-input-of-the-function-is-a-distribution

回答： Torsten 2018-1-15

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)

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Answer 1

Walter Roberson 2018-1-15

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https://ww2.mathworks.cn/matlabcentral/answers/377134-how-to-get-the-mean-of-a-function-when-the-input-of-the-function-is-a-distribution#answer_300140

编辑：Walter Roberson 2018-1-15

在 MATLAB Online 中打开

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: