# How can I calculate the moments of an exponential random variable

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Jaime De La Mota Sanchis il 14 Set 2022
Commentato: Torsten il 14 Set 2022
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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### Risposte (1)

Torsten il 14 Set 2022
Modificato: Torsten il 14 Set 2022
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 =
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Jaime De La Mota Sanchis il 14 Set 2022
Modificato: Jaime De La Mota Sanchis il 14 Set 2022
Thank you very much for the help. Is there a way to do this with other random variables?
Torsten il 14 Set 2022
Sure, you only need the PDF of the distribution and the fact that an analytical expression for the moments exists.

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