Statistics

4. Time to an accident after purchasing a car is distributed according to the density function: f(y) = (7 -3y) 1 16 y E (0 , 2 ) 1 16' y E (2, 10) = 0 otherwise (a) [4 pts] Calculate the distribution function F(y) by giving its values for y 10 (b) [2 pts] Is it more likely to have an accident in the first 2 years or in the years 2-10 after purchase? (c) [2 pts] The cost of an accident is 10,000 if it happens during the first 2 years, and 2,000 if it happens during the years 2-10. What is the expected cost of an accident? (d) [4 pts] Find the expected time to an accident