Based on historical evidence, Tucson\'s monsoon thunderstorms fall into three ca

Question

Based on historical evidence, Tucson's monsoon thunderstorms fall into three categories. Approximately 60% of the storms cause no flood damage, 35% cause only minor damage, and 5% cause major flood damage. On average, a storm that causes minor damage results in property damages that are uniformly distributed between $20K and $100K, while a storm causing major damage results in property damages that are uniformly distributed between $100K and $1,000K.

(a) What is the expected cost of flood damages associated with each monsoon storm?

(b) What is the variance of these flood damages?

(c) What is the expected cost of flood damages associated with a storm, given that causes damages?

Explanation / Answer

Consider the table:

Here,

variance = E(x^2) - E(x)^2 = 1.64*10^10 - 48500^2 = 14,032,750,000 [answer]

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b)

As it is given that it causes damages, and

P(damage) = 0.35 + 0.05 = 0.40

Then we divide the P(x) column by 0.40, then consider only the last 2 rows.

Thus,

E(x|it causes damages) = Sum(x P(x)) = $121,500 [answer]

x P(x) x P(x) x^2 P(x) 0 0.6 0 0 60000 0.35 21000 1.26E+09 550000 0.05 27500 1.51E+10 Totals 48500 1.64E+10 Mean 48500 Variance 14032750000

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