Homework_03_Solutions

# Homework_03_Solutions - STA 100 Homework 3 Due 5:00pm Wed...

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STA 100: Homework 3 Due: 5:00pm, Wed 2nd February Assigned: Thursday, 27th January (Details will be covered in class on Friday January 28th) For all questions you must show your working. This enables us to understand your thought process, give partial credit and prevent crude cheating. Please see the code of the conduct in the Syllabus for rules about collaborating on homeworks. 1. Poisson Probabilities: Lyme disease is a bacterial infection transmitted through tick bites. While relatively common in large parts of the northeast US, cases in northern California are still reported. The number of cases in northern California each month is assumed to follow a Poisson distribution with mean 5. (a) Compute the probability of no cases of Lyme disease in a month. P ( X = k ) = λ k k ! exp( - λ ) λ = 5 ,k = 0 exp( - 5) = 0 . 006737947 (b) Compute the cumulative probability of 9 Lyme disease cases in a month (i.e., the prob- ability of 9 or fewer cases). 9 X k =0 λ k k ! exp( - λ ) = 0 . 968172 (c) Compute the probability of 10 or more cases of Lyme disease in a month. P ( X 10) = 1 - 9 X k =0 λ k k ! exp( - λ ) = 1 - 0 . 968172 = 0 . 03182806 (d) What is the expected number of cases of Lyme disease in a month? E ( X ) = λ = 5 (e) What is the standard deviation of the number of cases of Lyme disease in a month? SD ( X ) = p V ar ( X ) = λ = 2 . 236068 (f) To ensure that the state is prepared for a possible spike in cases, they have an emer- gency procedure to that kicks in if the number of reported cases exceeds a threshold. The threshold (denoted by

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Homework_03_Solutions - STA 100 Homework 3 Due 5:00pm Wed...

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