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How can I calculate the moments of an exponential random variable

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Jaime De La Mota Sanchis
评论： Torsten 2022-9-14
Hello everyone.
I am working in an aplication related to polynomial chaos expansions. For that, I need to calculate the analytic moments of the following random variable
pd = makedist('Exponential', 3)
t = truncate(pd,0,5)
rand_num=random(t, 100000000, 1);
However, I have no idea on how to do it. Can someone please give me a clue?
Best regards.
Jaime.

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回答（1 个）

Torsten
Torsten 2022-9-14
编辑：Torsten 2022-9-14
Ran in:
syms mu x lower upper n
assume(n,'integer')
assume(n>0)
lower = 0;
upper = 5;
mu = 3;
f = 1/mu*exp(-x/mu) / int(1/mu*exp(-x/mu),x,lower,upper)
f = 
fplot(f,[0 5])
%Check
int(f,x,lower,upper)
ans = 
1
%Moments
moments = int(f*x^n,x,lower,upper)
moments = 
  2 个评论
Jaime De La Mota Sanchis
Jaime De La Mota Sanchis 2022-9-14
编辑：Jaime De La Mota Sanchis 2022-9-14
Thank you very much for the help. Is there a way to do this with other random variables?
Torsten
Torsten 2022-9-14
Sure, you only need the PDF of the distribution and the fact that an analytical expression for the moments exists.

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