Hello I am a math major doing a stats minor currently in undergrad. I am understanding the motivation and derivation of moment-generating functions but I am having trouble understanding what a moment means when the $k>2$.
If I am correct I believe moments are just statistical parameters like, mean, variance, and so forth. (Correct me if I am wrong!)
with $k=1$ we get $E(X)$ and with $k=2$ we get $E(X^2)$ which is not necessarily variance but we can easily find it if we have $E(X)$ since $Var(X) = E(X^2)-(E(X))^2$.
But now I am having trouble understanding what the moments of $k>2$ imply or how can we use them to find such parameters. Your help and expertise would be appreciated!