Monte Carlo Integration - Expected value of a function

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Alexis Villacis
Alexis Villacis 2019-2-21
Hello community,
I estimated this corn production function using data on corn yields and fertilizer
Y = min ( a + b*x , c)
where Y is yield and x is the amount of fertilizer.
Now I want to estimate the expected value of this function using monte carlo integration.
The data I used for estimating this function have x in the range of [0 200].
So I coded this:
%%
%Define size of sample
n=1000000
%Generate uniformly distributed random numbers in the interval (0,1) and de
u = rand(n,1)
%Define random points in the interval of fertilizer applied [0 200]
f = 200*rand(n,1)
%% Evaluate the function at the different random points
Y = min( a + b*f , c );
%%Obtain the average of the evaluations
meanY = mean (Y)
When I do this I get a pretty reasonable result.
My question is:
Do I have the evaluation of the function at the different random points right?
I've been reading and it seems that I need to correct my evaluation, because my fertilizer data come from the range [0 200] such that the evaluation of the function should be:
Y = 200 * min( a + b*f , c );
but when I do this, the value of my expectation (average of the evaluations) does not make sense (it increases 200 times).
Any help will be appreciated.
Thank you!

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