Question

***Please do as early as possible***

TRP 525 TRANSPORTATION STATISTICS AND RESEARCH

During a 2-month hurricane season, severe hurricanes at a given location occur at Poisson times with a rate λ= 1 event/month. Last year, 4 hurricanes occurred and the local press has blamed “changes in the climate” for what they reported as an extremely severe hurricane season. From a statistical point of view, how unusual are seasons of this or higher severity? Would you agree or disagree with the press that this was an exceptionally severe season?

Answer 1

Here the Poisson tims rate = 1 event/month

so for two month the expected number of hurricanes = 1 * 2 = 2 Event

so here there are 4 hurricanes occurred.

Now, we have to find the probability of such event happening

Pr(x >=4) = 1 - POISSON(x < 4 ; 2)

= 1 - [e^-2 2⁰/0! + e^-2 2¹/1! + e^-2 2²/2! + e^-3 2³/3! ]

= 1 - [0.1353 + 0.2707 + 0.2707 + 0.1804]

= 1 - 0.8571

= 0.1429

so here the probability is not so unusual as it is greater than 0.05 so we would not agree with the local press.