Question

A randomly selected competitive cyclist takes performance enhancing drugs with probability use. If Chris doesn't use drugs 0.1. The cyclist Chris Crumb is tested each week for drug then his test score each week follows a Pois(5) distribution. If Chris does use drugs then his test score each week follows a Pois(15) distribution. Each week's test score is independent To answer this question you may use the numbers from the following Rstudio output, but give all your workings to obtain full marks. must (dpois (9,1ambda=5))^50 [1] 9.4e-73 (dpois (9,1ambda=15))^50 [1] 3.4e-75 dpois (18,1ambda=5) [1] 4.0e-06 dpois (18,1ambda=15) > [1] 0.07 (a) Chris's test result was 9 each week for 50 weeks. What is the probability that this happens if Chris doesn't takes drugs? (b) What is the probability that Chris takes drugs, given the test scores from part (a)? (c) In the 51st week, Chris returns a test score of 18. Now what is the probability that Chris takes drugs?

Answer 1

Solution:- X cletemine the test Score yclrst chrisE aumb tor each weer chris not using chvgs chis using gruqs Y,O cletermíne determine Pof (5) X1 y o poi (1s) XIy= (a) chris test dsuits uai 9 each wceR K50 eeks. Here P dngs chrig docir use PLx-y50 , Test Scores of each eek is independer e**.5)1 So 94e 3 Cb) p Sb ueets daugs Ix. 9 jor chrig uses weets P(v9 for 50 weer9 weersyo] Py6 IPLPX-9 for so weets P(x -9 foY So ( Sin:e ue Baye heoom 0. 000 401

PLehris weet (C) Use drugs x- 18 in sst [y-1x- 18 n sisweek P P[x lP(y PytP[x-18 |y-0] PLy-) Plx: 18y 09 1& ! 0-999 486