at an average rate of A vampire hunter encounters vampires of encounters follows

Question

at an average rate of A vampire hunter encounters vampires of encounters follows one vampire every 8 months. Assume the rate a Poisson process. What is the probability of more than 1 year passes before 3 vampires are encountered? What is the probability of no encounters in a 2 year period? What is the expected amount of time to encounter 10 vampires? The life expectancy in years of a Vampire can be modelled with a Weibull distribution with = 95 and =1/3 What is the 85th percentile for Vampire's ages? What is the expected life expectancy for Vampires? What is the variance of life expectancy for Vampires? What is the median life expectancy of Vampires? What is the probability a Vampire lives between 100 and 600 years?

Explanation / Answer

1)a) Exponential distribution

= 3vampires per 24 months = 3/24

P(X > 12) = (1 - (1 - e-x)) = (1-(1-e-(3/24)*12)) = 0.2231

b) = 1/8 = 10/80

Mean = 1/ = 80 months for 10 vampires

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