How can I calculate the moments of an exponential random variable

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.

Answer 1

[Torsten]

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 = 

[Jaime De La Mota Sanchis]

Thank you very much for the help. Is there a way to do this with other random variables?

[Torsten]

Sure, you only need the PDF of the distribution and the fact that an analytical expression for the moments exists.