The moment generating function definition you have used is for a continuous random variable with probability distribution .
In every case we can use the definition: .
So in your case:
We went over this material once in class and we have a bunch of problems that we have to do, and I still don't know if I understand the concept fully. One of the problems is:
Find the moment-generating function of the discrete random variable X that has the probability distribution
f(x) = 2(1/3)^x for x = 1, 2, 3, ...
and use it to determine the values of mu1' and mu2'.
So I tried to use the definition, which says that Mx(t) = E(e^(tx)) = Integral from -INF to INF of (e^(tx))*f(x)dx.
I got the Integral from 1 to INF of (e^(tx))*(2(1/3)^x)dx, but now I am lost... any help would be GREATLY appreciated.
It's called Latex and it isn't a program. It's built right into this site so any user can use it.
You see the button beside the YouTube button when you make a post? That button wraps the selected text with [tex] tags.
You can also click on the math equations you see on here to find out how they were written. For example, to write:
I would have to write:
\sin {\sqrt {4x^2}} = \log {\frac {1}{2}}
And then wrap it with math tags.