13. [14 marks) For a driver with a given accident rate of r per year, the number of accidents in which he is involved in

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13 14 Marks For A Driver With A Given Accident Rate Of R Per Year The Number Of Accidents In Which He Is Involved In 1 (20.68 KiB) Viewed 69 times

13. [14 marks) For a driver with a given accident rate of r per year, the number of accidents in which he is involved in a year has a Poisson distribution with mean r. The accident rate r of a randomly chosen driver follows a distribution with probability density function 2er (2)al 1.) r>0, a>0, 2>0. r(a) Let X be the number of accidents in which a randomly chosen driver is involved in a year. (a) (17 marks) Derive the probability mass function of X? (b) (3 marks) Find P(X = 2) if a = 7 and 2 = 3.2. a