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.

1. What is the variance of these flood damages?

2. 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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