I'm reading a stat textbook and it says the following: Let a discrete-time random walk be defined by Xt = Xt-1 + et, where the et's are i.i.d. normal(0,σ2). Then for t≧1, (i) E(Xt) = 0 (ii) Var(Xt) = t σ2 However, the textbook doesn't have a lot of justifications for these results and I don't understand why (i) and (ii) are necessarily true here. For example, E(Xt) = E(Xt-1 +et) = E(Xt-1) + E(et), but how can you calculate E(Xt-1)? Can someone please explain in more detail? Thanks a lot!