c. Find Elt) anU 4.22 4.26 Predicting when a Florida hurricane occurs MCANE anal

Question

c. Find Elt) anU 4.22 4.26 Predicting when a Florida hurricane occurs MCANE analysis of damages caused by Florida hurricanes 3.12 (p. 140). In an effort to minimize the mone that result from a devastating Florida hurrican the researchers' analysis included a graphic sho sequence number of tropical storms within a are most likely to develop into a hurricane. Data hurricanes are summarized in the table. Let x rep the sequence number of a Florida tropical storm wi season that develops into a hurricane ty Par showin fo Number That Develop into Hurricanes Sequence of Storm 10 Source Based on Malmstadt, J. Scheitlin, K &Elsner.; J. Florida Hurricanes and Damage Costs" Southeastern Geographer Vol. 492·Summer 2009 (adapted from Figure 3). a. Explain why x represents a discrete random variable b. Specify the probability distribution for x. c. Find P(x = 5). d. Find P(x

Explanation / Answer

a. x represents a discrete random variable beacuse it takes specific values of x only not every value, in this case it is integer only.

b. Probability distribution of x

(c) P (X =5 ) =  0.1642

(d) P(x < 5) = P(X = 1) + P(x = 2) + P(X = 3) +P(X = 4)

= (4 + 10 + 5 + 6)/ 67 = 0.373

(e) E(x) = xp(x) =

so E(X) = 6.1194

and we can say there are mean number of 6 number of storms within a season that develps into a storm.

(6) P(X >15) = 1/67 = 0.015

so it is very less and lesser than 0.05 so it is very least likely to observe a hurricane after the 15th tropical storm of the season.

sequence of storm Hurricane number p(x) 1 4 0.0597 2 10 0.1493 3 5 0.0746 4 6 0.0896 5 11 0.1642 6 5 0.0746 7 5 0.0746 8 5 0.0746 9 4 0.0597 10 2 0.0299 11 5 0.0746 12 1 0.0149 13 1 0.0149 14 1 0.0149 15 1 0.0149 22 1 0.0149

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