Pls answer question A6 and explain 2013 x 2014 x C For A X apers public/2013 201

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Pls answer question A6 and explain

2013 x 2014 x C For A X apers public/2013 2014/MA/2013 2014 ST236 1 1 2.PDF (a) 0 (b) 1/3 (c) 1/2 (d) 2/3 (e) 1 A6. The annual number of invitations to give international conference talks reeeived by an ageing professor has a Poisson(6) distribution, r 0, 1, 2, 3, in past years, the average mirnber of invitations received per year was 2. How- ever, this year he has received invitations. Based on this single o ot r 4, what is the value of the likelihood ratio test statistic for testing the hypoth eis that the professor has suddenly Ren a Ixuel in his international standing, i teltiug He 2 against 2 (a) it raidon AT. Fo kelily tested and founir

Explanation / Answer

for

= 2

and x= 4

P1(X) = 24*e-2 / 4!

For single observation

= 4

x= 4

p2(x) = 44e-4 /4!

ratio P1(X) / P2(X) = 24*e2 / 44   = e2/16

hence correct answer is c

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