Question: = 1 and Var[X] = (a) Let (n) nN be a sequence of i.i.d. random variables with E[X1] (0, 0). Show that where Tn=1

= 1 and Var[X] = (a) Let (n) nN be a sequence of i.i.d. random variables with E[X1] (0, 0). Show that where Tn=1 Xi. - ()N(0,1), (b) Now let (Xn) nEN be a sequence of i.i.d. random variables with X Tn=X; fulfills n(Tn -n) N(0, 1). n (c) Let Y~Pois (A) with > 0. Use part (b) to show that -(-A) x+V N(0, 1). 818 (d) Use (b) to show that lim e -n k=0 k! *Wi 12 ~ Pois (1). Show that

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