Hi,

I'm stuck with this question about 2d random walks on Z^2

Let S_n = (X_n, Y_n) be a simple symmetric random walk in Z^2, starting from (0, 0), and set T = inf {n >= 0: max{|X_n|, |Y_n|} = 2}. Calculate E(T) (Expectation of T).

How would I proceed? would i just use the standard definition of expectation? if so, i would need to work out P[T=n] for natural numbers n yes? but how would i work this out, there are too many possibilities!!!! Is there a formula for this?

Thanks