Question

4 S and Gy(s) Consider the following two probability generating functions Tx(s) 1-2s 1+3s respectively for the random variables Xand Y a) Find the expectations of the random variables X and Y b) Find the probability that X-0; c) Find the probability that Y 0; d) Find the probability that X+Y 0;

Answer 1

NO 0 Solubion B- Given tfad proleabtygenesatirg furetion Gys) ard +3S -2S ardon Vaables ECx ds ds C-2 C-1. -2) ds Sa 2 2S S2 |

NO-2 d ECy) ds S2 ds +as) .- S.3 S l3S-3S S 1+33 L 4 I6 T o) PLx0) b) K 0,, 2- -- 4 S0 Pixo) -xo)

Pogk NO-3 Gylo) (c) PlY0) only indepertrt TRan d) T x ard y are Used Can be irdaperdent then x and y Let P GP by given be COun PCx)Hy)