Please provide all steps so I may follow along. Please do not provide excel only

Question

Please provide all steps so I may follow along. Please do not provide excel only solutions, as I'd like to see the steps.

Losses $                                                                        Probability of Loss

$0                                                                                                      0.60

$100,000                                                                                      0.20

$200,000                                                                                      0.10

$500,000                                                                                      0.06

$1,000,000                                                                                 0.03

$5,000,000                                                                                 0.01

1) Find the average or expected loss of the group of buildings in a given year.

2) Calculate the standard deviation of the distribution.

3) Find the Coefficient of Variation.

Explanation / Answer

a) Expected loss = xf(x) = $0 * 0.60 + $100,000 * 0.20 + $200,000 * 0.10 + $500,000 * 0.06 + $1,000,000 * 0.03 + $5,000,000 * 0.01 = $150,000.

b) Variance 2 = x2f(x) = 0 * 0.60 + (100,000)2 * 0.20 + (200,000)2 * 0.10 + (500,000)2 * 0.06 + (1,000,000)2 * 0.03 + (5,000,000)2 * 0.01 = 301000000000.

Standard deviation = 301000000000 = $548,634.6689.

c) Coefficient of Variation = / = $548,634.6689 / $150,000 = 3.6576 or 365.76%.

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