calculations

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Calculations
Question 1
The Annual loss function is shown as u=1-exp⁡(0.3x)The maximum premium function for the risk is derivative of the equation given.
The cost of the arena is given $900 million. The probability distribution function for the approximatio is as represented below:

Whereby the value of x is given as the annual loss in dollars
K is the shape parameter, and γ is the scale parameter.
The integral of the function is given as the
integral =
Substituting the value of u from the annual loss equation, u=1-exp⁡(0.3x) =1-exp-0.3×2=0.8222The maximum premium is thus fx=1.560.822^26×21.5-1e-0.82226×21.5=$12,000million
Question 2
Amount of the net cost if lost = $125,000
Probability of losing = 0.2
The probability of taking legal action is 0.3
The probability of rumor being true = 0.9
Current probability of rumour = 0.5
The possible causes of the action include
Leaving the story
Publishing the rumor
The hiring of a private detective to scrutinize the rumor
Cost of the private detective = $10,000
Extranet income = $ 50,000
The possible solution is to hire the private detective to investigate the rumor then take the decision either to publish or not. The best engineering solution depends on the probability of occurrence of the alternatives and the losses involved (Leon-Garcia, 90). The amount of money they should be prepared is given as below
10,000+0.2×50,000+125, 000=$145,000
Works Cited
Leon-Garcia, Alberto. “Probability, statistics, and random processes for electrical engineering.” (2017).