Question

 In Istanbul, on average, 6 Leveche (lodos) occur every year. (a) What is the probability that in a given year, number of lodos is fewer than 4 in Istanbul? (b) What is the probbaility that in a given year, number of lodos is from 6 to 8 in Istanbul? 

Answer 1

This is a Poisson distribution with $\mu=6.$

(a) $P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X+3)=$

$=e^{-6}(\frac{6^0}{0!}+\frac{6^1}{1!}+\frac{6^2}{2!}+\frac{6^3}{3!})=0.1512.$

(b) $P(6\le X\le8)=P(X=6)+P(X=7)+P(X=8)=$

$=e^{-6}(\frac{6^6}{6!}+\frac{6^7}{7!}+\frac{6^8}{8!})=0.4016.$