Bonus problem. Suppose X1, ..., Xn are iid Poi(1). Then The mean is 1 and the variance is also 1. Zn = Vn(X - 4) = Vn(X - 1).The MGF of Zn is vz, (t) = Eletvn(X-1)]. Following the arguments in the handout 6 (pp 22-23) to directly show that if n - oo t2 log( 2/Zn (t) ) 2 You may find the following results are helpful in your calculations the MGF of Poi(1) is Eletxi] = eet-1 2-2 ex = 1+x+ J...+ + ... 2! K