X ∼ NBD(r, p). Derive the var(X).

Expert Solution

Negative Binomial Distribution :

A negative binomial arbitrary variable is the number X of rehashed preliminaries to create r achievements in a negative binomial analysis. The likelihood appropriation of a negative binomial irregular variable is known as a negative binomial distribution The negative binomial conveyance is otherwise called the Pascal distribution

. 5 0.1 05 0.4 • 10 0.4 Ics Scated with O n 20 40 80 100 120

Solution : XN NBD, Derive the Varcx) xa Negative Binomial olishbution If XN NBD CY, P) then what is varex) the We Jenow that since we have t = x,+ X2+ ---- Where xi is a geometric random Variable Scanned with CamScanner

E(X)= E(X) + ECXX) + ---- E(Xo) Since E(XP). therefore E(X)= petit so there fore. E(X= m ( EXP Where P - probability of success on an Individual A trial. ExeoThe no.or trials required to producer! succes in a negative binomial distribution. so, we got expected mean value of E(X)= Similarly Variance. L V (X;)= (1-P) i Tvar[x] = 7C1-P 17 x NBD(OP) (1-P) = probability of failure of an individual I trial C-p]

milcah answered 1 year ago

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