do not answer this statistics and probability question.

1. Let X1, X2, .. " a sequer of i. . N(u 2) random v oles, where u 0 and 0 0 (ii) X, Exp(J ), 0 r 3. Let X. op; (ii) " chen+D El=1i2 X - Hasn - . . 4. Let ' },21 be a sequence of inde adent random variab' , such that the p.m.f. of in i's given by ful = ONIP .fx e ( - n' ni) . otherwi : Show that X, - 0, ar . - co, whe X, = =[" X,,n = 1, 2, . 5. Let Xn ~ NB( , Pn), where In E (0,1), n . 1, 2, .. . and lim,-. n (1 - Pn) = 1 0. Show th .( X, - X ~ F A), the Poisse distribution with mean 1