2. An automobile manufacturer is concerned about a fault in the breaking mechanism of a particular model. The fault can on rare occasions cause a catastrophe at high speed. Assume that the distribution of the number of cars per year that will experience the fault is a Poisson random variable with mean 6. What is the probability that: i. Six cars will experience a catastrophe in a year? ii. Four or fewer cars will experience catastrophe per year? iii. Three cars will experience catastrophe in six month? iv. Two cars will experience catastrophe in a year and six month? v. Compute the variance and the standard deviation associated with the cars that will experience a fault in a year. vi. The coefficient of variation with the cars that will experience fault in a year