Question

Le 1 Suppose that you have a random valables x, and X2 whose distribution are Poisson with parameters n and a respectively Let y = x, + X2, then 2) Find the probability generating function of y. b) Find probability devity function of y. (Pmf) c) Find non factorial moment of y. Do.

Answer 1

a) The PGF & Y , Py(s) : E( ); where ISIS 2E 3 X1 +*2) ESI 52) 2 EC5*") E (842) Can Xi and X2 are inelebe) 4 3 8 2. -12- 2 2 3 stret 7420 12 re-rico-s). < => -). zę -@tra-(Myoma) s) Pycs) .e (miesz) bi-s) b) - The PME of it is given by; - Plyok) i pul is) Iseo [ where pics) denote .. .k the durivaline of Now , 32-0 & Py68) 2e-Citro) (-52 (2,4 123 xen la se lienes.(Alema) . * 276) 2" (Aves)C-5) (Siena) i Isco IS20 ... so on . Then we get per colocou Dy (9) Wsco ze Potra! (14x2) ....)

Now, Plyek) z Py®(s) . Szo LR ze -&rex (x1+x2)" :y. k ;k20/11...o from jy Poisson Calex2) facterial moment is given by, . Now the nth he nth factorial denote te with factorial derivative of Pyls) ze-61472)61-5) 14 da) dici 2 (i+ x2) *m