Hi everyone,

modelling stock prices I have the following generalized Wiener process:

Applying Itô's lemma gives us:

with being a standard normal random variable with mean 0 and variance 1. Taking exp of the above, gives us:

That gives us the expected value of S_t which I don't understand.

Specifically my question is: Why is the expected value of

with X being a normal random variable with mean and variance .

Thank you for explanation/proof, but also for relevant literature.