Let the value of your car be M dollars. (M can be, for example, 2000 but it is easier to write mathematics with M than with long numbers.) When you get into an accident, the amount of damage to your car is X dollars, where X is a random variable with probability density function f(x) = ( 2(M x)/M2, 0 x M 0, x < 0 or x > M. You have insurance with an M/2 dollar deductible. This means that if X M/2 then you pay the full amount of damages, while if X > M/2 then you pay M/2 dollars and the insurance company covers the remaining X M/2 dollars. Let Y be the amount you pay for the damage. (a) Find the cumulative distribution function of X. (b) Give a formula that expresses Y as a function of X. (c) Find the probabilities P(Y y) for y < M/2, P(Y = M/2), and P(Y y) for y > M/2. Based on these, write a formula for and sketch the graph of the cumulative distribution function FY of the random variable Y . (d) Find the probability P(Y < M/2). HowDoes