Hi, can you help me to solve this question? I have some confused. Please do not copy chatgpt! Thanks! Here is a quick crash-course on how deductibles work. Suppose the insurance policy you purchased on your car comes with a $500 deductible. Then, if you get into an accident the amount you have to pay out-of-pocket follows the following scheme: if the true cost of damages is under $500 then you pay the full cost of damages, but if the true cost of damages is over $500 then you only pay $500 (and your insurance company pays the rest). So, if the true cost of damages is say $1,000 then you only pay $500. Suppose now that your deductible is m, where m is a fixed positive constant. Let X denote the true cost of damages of a particular accident, and let Y denote the amount of money you actually pay as a result of that accident. Further suppose that X is well-modeled by an Exp(λ) distribution for some λ > 0. (a) Express Y as a function of X. In other words, find an explicit formulation for the function g(x) such that Y = g(X). (b) What is the expected amount of money you will have to pay? (c) Find FY(y), the cumulative distribution function (CDF) of Y. A Few
Hi, can you help me to solve this question? I have some confused. Please do not copy chatgpt! Thanks!
Here is a quick crash-course on how deductibles work. Suppose the insurance policy you purchased on your car comes with a $500 deductible. Then, if you get into an accident the amount you have to pay out-of-pocket follows the following scheme: if the true cost of damages is under $500 then you pay the full cost of damages, but if the true cost of damages is over $500 then you only pay $500 (and your insurance company pays the rest). So, if the true cost of damages is say $1,000 then you only pay $500. Suppose now that your deductible is m, where m is a fixed positive constant. Let X denote the true cost of damages of a particular accident, and let Y denote the amount of money you actually pay as a result of that accident. Further suppose that X is well-modeled by an Exp(λ) distribution for some λ > 0. (a) Express Y as a
Hints: • Consider three cases: y < 0, 0 ≤ y < m, and y > m • In each case, relate the
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