Question

(adapted from Ross, 4.60) Suppose that the number of times that Vampire Bill gets attacked by Hep V in a given year is a Poisson random variable with parameter ? = 5. Now, he discovered a new drug (based on large quantities of vitamin C) that has just been marketed to protect from Hep V. It claims to reduce the Poisson parameter to ? = 3 for 75% of the population.

For the rest of the population, the drug has no appreciable e?ect on Hep V. If Bill tries the drug for a year and only had 2 Hep V attacks in that time, how likely is it that the drug was bene?cial for him?
(please show all work and steps thank you!

Answer 1

The probability of getting attached by Help(v) without benefit of new drug = p(A) * The probability of getting attached by Help(v) with new drug = p(B) Therefore, Hence the probability that help attack are z given he is without benefit of drug is = P(c/A) = e^- lambda lambda ^x/x! Where, lambda = 5 , x = 2 P(c/A) = 0. 084 The probability that Help v attack are 2 given he is with new drug = P(c/B) = e^- lambda lambda^x/x! Where, lambda = 3 , x = 2 implies substituting the values in above Equation then O(c/B) = 0. 224 Hence the probability of Help v attack are 2 = P(c) = p(A) *p(c/A) + p(B) *p(c/B) = 0. 25*0. 084 + 0. 224* 0. 75 = 0. 189 The above probability that drug is benificial given greaterthanorequalto gad 2 Hep v attacks implies p(B) *p(c/B) /p(c) implies 0. 224 * 0. 79/0. 189 implies 0. 8889