# expected value of a function

Possible Duplicate:
sub martingales and more

Can someone help me compute the expected value of $X_{n+1}$, that is : $E[X_{n+1}| X_0,\dots,X_n]$?

Given : $X_n = X_0 e^ {\mu S_n}$, $X_0 > 0$

where $S_n$ is a symmetric random walk and $\mu$ is greater than zero.

I am aware that the expected value of a given function is the mean. But i would like to know a method to compute the above. What is the right approach to get started on such problems on expected value computation.

Update:

I understand that $X_{n+1} = X_n \cdot e^{\mu (S_{n+1} – S_n)}$ ? How do I proceed with computing the expectation?

#### Solutions Collecting From Web of "expected value of a function"

Hint: $X_n = e^{\mu Y_n} X_{n-1}$ where $Y_n = S_n – S_{n-1}$ is the $n$’th step of the random walk.