Exercise 12.6 Let {Xn} be given by (12.11) and define Wn = n i=1 Xi. Under the

Exercise 12.6 Let {Xn} be given by (12.11) and define Wn =

Σn i=1 Xi.

Under the relations σ2Δt = (Δx)2 and t = nΔt, show that the MGF of Wn is given by

for some an such that limn→∞ an = 0, hence

It follows that Wn converges in law to a random variable X(t) ∼ N(μt, σ2t).

Transcribed Image Text:

mn(s) = n = [1 + uts+o2ts2/2+ an 1+ n