Question

Based an lisbical data, he aar number ot damage -causing hait stotns That occur at a por hicuworSacmm, per Neaur is 6.54t. Based on this vearty avemae calauoue ne sollasin prolodblihes, and rand caon ansuas to he nearest Pthne will le mne n a damag-cassi Hailstorms at this sarm, unrg tu nx b)mon then naus ot the next 4 yeads will be free ot anv damate -causiag hailstotms)

Answer 1

a)

rate = 0.54/year

for 3 year

$\lambda$ = 3 * 0.54 = 1.62

${\displaystyle P(k{\text{ events in interval}})=e^{-\lambda }{\frac {\lambda ^{k}}{k!}}}$

P(X > 2) = 1 - (P(X = 0) +P(X = 1) + P(X = 2))

= 0.22182

b)

more than half of next 4 years will be free of hailstorm

= P(X = 0 in next 2 years)

= e^(-0.54*2)

= 0.33959