1. A data regarding automobiles accidents in which a child (under age 5 years) was in the car and at least one fatality

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1 A Data Regarding Automobiles Accidents In Which A Child Under Age 5 Years Was In The Car And At Least One Fatality 1 (325.68 KiB) Viewed 28 times

1. A data regarding automobiles accidents in which a child (under age 5 years) was in the car and at least one fatality occurred is reported below in terms of joint probability density function. The study from which data was obtained focused on whether or not the child survived and what type of seatbelt (if any) the passenger used. Define two random variables X= 0, if the child survived 11, if not 0, if no belt used Y = { 1, if adult belt used 2, if car-seat belt used. Note that X is the number of fatalities per child and, since children's car seats usually utilize two belts, Y is the number of seatbelts in use at the time of the accident. у f(x,y) 0 1 2 0 0.38 0.14 0.24 X 10.17 0.02 0.05 (a) Find the covariance between X and Y. Conclude whether or not survival in car accident depends on the use of seatbelt. Justify your arguments. (b) Find the probability that a child survived in car accident. (c) What is the probability that a child survived given that he or she was in a car-seat belt? (17 marks)