Please help me solve this microeconomic question.Thank you

A company is analysing the number of accidents that occur each year on the factory floor. It believes that the number of accidents per year N has a geometric distribution with parameter 0.8, so that: P(N - m) - 0.8x 0.2", n - 0,1,2. .. For each accident, the number of employees injured is Y, where Y= X +1, and X is believed to have a Poisson distribution with parameter 2.2. The company has taken out an insurance policy, which provides a benefit of $1,000 to each injured employee, up to a maximum of three employees per accident, irrespective of the level of injury. There is no limit on the number of accidents that may be claimed for in a year. (i) Show that E(5) = 0.634 and var( S) =2.125, where S is the total number of employees claiming benefit in a year under this policy. [7] (ii) Hence find the mean and variance of the aggregate amount paid out under this policy in a year. [1] [Total 8]