Probability and Statistics 2. [4 pts] The number of times that an individual con

Question

Probability and Statistics

2. [4 pts] The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter 1 = 3. Suppose a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to 1 = 2 for 75% of the population. For the other 25% of the population, the drug has no appreciable effect on colds. If an individual tries the drug for a year and has no cold in that time, how likely is it that the drug is beneficial for him or her? Hint: Use Bayes' theorem.

Explanation / Answer

P(no cold) =P(drug effective and no cold+not effective and no cold) =0.75*e-2+0.25*e-3 =0.1139

therefore P(drug is effective|no cold) =P(drug effective and no cold)/P(no cold)

=0.75*e-2/0.1139 =0.8908

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