Question

A randomly selected competitive cyclist takes performance enhancing drugs with probability 0.1. The cyclist Chris Crumb is tested each week for drug use. If Chris doesn’t use drugs 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 must give all your workings to obtain full marks.

> (dpois(9,lambda=5))^50
  [1] 9.4e-73
  > (dpois(9,lambda=15))^50
  [1] 3.4e-75

  > dpois(18,lambda=5)
  [1] 4.0e-06
  > dpois(18,lambda=15)
  [1] 0.07

1. (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?

2. (b) What is the probability that Chris takes drugs, given the test scores from part (a)?

3. (c) In the 51st week, Chris returns a test score of 18. Now what is the probability that Chris takes drugs?

Answer 1

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18 in 5st 3.e2 heek x-18 P[x- 1BLy- PIy in 15 I5 13 -5 -1S 181