Question

3. Demonstrate that the negative binomial distribution is a member of the (a,b,0) class.

please write legible

Answer 1

In preob. theory, the disteri lection of a discrete se. v. N whose values are non-negative entegere is said to le a member of the Ca, bio) class of dist if the pmf. obeys 2 af k=1,2, 3, = P[w-u] . [provided af besist and are scall

P[a]. (*) 4K-1 6- K Hence the ) 1=0,1,2,... q=1-p- - العام & Negative Puri 12+ x-2 Otk-2 K -1 - pr+k-)! KI (+4-2)! otka q. = qt (8-1)q K. azq; b = (x-1) a ..

Hence the pmf obeys the condition of (a, 6,0) class- a Negative leinomial dist belongs to (0,6,0) class.