A manufacturer produces laptops with variable quality. In fact, for each laptop, itsquality level A has a Gamma distribution with shape parameter a > 0 and rateparameter B > 0, that is, A has density functionBafa(A)T(a)where I' is the Gamma function. It is not necessary to know properties of the Gammafunction to answer this question.If a laptop has quality level A, then it crashes X times a day, where X has a Poissondistribution with parameter A.Given that a laptop crashes x times today, what is the conditional probability densityof A, fajx(^|æ)?Baxª–1e-BAr(a)а.Ob.T(a)pata-z-1r!e-(B–1)Ar(a)c.-I-paDa-2 (x + 1)e-BAГ(а)d. O e. (B+1)“1z+a-1e-(B+1)AГ(а)O f. 1z+a-le-(B+1)\gaT(a)Bag.r(a)O h. none of the other options are correctO i. Ae-Aa!(B+1)ª+zA++a-1e-(B+1)AI(a)Oj.paO k.r(a)O I. (1+B)ª+#I(r+a)++a-1e-(B+1)A

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A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A manufacturer produces laptops with variable quality. In fact, for each laptop, its quality level A has a Gamma distribution with shape parameter a > 0 and rate parameter B > 0, that is, A has density function Ba fa(^) I(æ)