How can i get the mean of the function using symbolic maths in MATLAB

i am interested to find the mean of the distribution but I am unable to get it.Could anybody help me to figure out where I am doing the mistake?

f=@(a,b,x)1./(x*b*sqrt(2*pi)).*exp(-((log(x)-a)./(sqrt(2)*b)).^2)

I am interested to find E(X) in symbolic form.

i know from the existing literature E(X)=exp(a+b^2/2) but i am not getting this answer. I am using the the function int(f,x,[0,inf]) by assuming that a is real value constant, b is greater and equal to zero.

Thanks

Answer 1

[John D'Errico]

Note that if P(x) is a PDF on the domain [0,inf], then the expected value of the corresponding random variable is gotten from

int(P(x)*x,x,[0,inf])

To start with, it looks like you forgot to multiply by x.

A quick look at the PDF shows that you seem to be looking for the expected value of a lognormal distribution.

[zahid]

Thank you very much John D'Errico for answering this question i did this but i am getting the following answer int((2251799813685248*exp(-(a - log(x))^2/(2*b^2)))/(5644425081792261*b), x, 0, Inf) which is not the same as required. Could you please this why?