In this exercise, we will compute expectations for a certain class of stochastic integrals, namely T E Jo f (W.) dWt (6.64) for an arbitrary but bounded function f: R - R. We wonder if there's a pattern, and if so, whether it depends on f. We have f(W+) dWt = lim Fn, (6.65) n-too where n Fn = f(W ( k-1)At) ( WkAt - W( k-1) At (6.66) k=1 and At = At(n) = T.Let M > Obe the bound of f, i.e. |f(x)| g M for all x 6 R Show that n |Pn| S E M |WkAt W(k1)At| (6-67) k=1 Compute the expectation of the right hand side, thereby showing that it is finite. (Hint: You may freely use the following fact: if Z is a standard normal random variable, then E [|Z |] = #3