Question

(14 pts) Clearly state which distribution you are using to arrive at your solution, for all parts of this question. Suppose that on average 4 tornados occur in 8 years in a county in Oklahoma. If the occurrence of tornados follows a Poisson process: (a) What is the probability that less than 6 years pass before 2 tornados occur? (b) What is the probability that there will be at least one tornado next year? (c) What is the probability that the time between successive tornados is greater than 3 years?

Answer 1

Mean=4tornadoes in 8 years=0.5tornado/year

a)To calculate this lets calculate and see what is the probability that atleast 6 years happen between two tornadoes.

$P(k=0)=\frac{e^{-0.5}0.5^0}{0!}=0.6065$

$P(T<6)=1-P(T>6)=1-(0.6065^6+0.6065^7+....)=$$1-\frac{0.6065^6}{1-0.6065}=0.8734$

$b)P(k\geq 1)=1-P(k=0)=1-\frac{e^{-0.5}0.5^0}{0!}=0.3934$

c)We need to know that the time between successing tornadoes is atleast 3 years. Which means each year there were no tornadoes. we know the probability of having no tornado as P(k=0)=0.6065

$P(T>3)=0.6065^3+0.6065^4+......=\frac{0.6065^3}{1-0.6065}=0.5671$