Kindly help me to obtain accurate solutions for the following questions.Thank you

The table below shows the cumulative incurred claims by year for a portfolio of general insurance policies, with all figures in fm. Claims paid to date total 13.5. The ultimate loss ratio is expected to be in line with the 2013 accident year, and claims are assumed to be fully developed by the end of Development Year 3. Development Year Accident Year 2 3 Earned Premiums 2013 3.01 3.38 1.85 4.00 4.32 2014 3.30 3.67 4.15 4.41 2015 3.32 3.86 4.55 2016 3.74 4.68 Calculate the total reserve required to meet the outstanding claims, using the Bornheutter-Ferguson method. [9] For three different risks, an actuary is modelling the monthly claim numbers with three different Poisson distributions. Risk Exposure Number of claims Risk 1 36 months 20 Risk 2 30 months 18 Risk 3 24 months 16 (1) Derive the maximum likelihood estimates of the parameter for each of the three individual Poisson distributions fitted. [5] (ii) Test the hypothesis that the three risks have the same monthly claim rate. [5] [Total 10]Consider the following probability density function: h(x) =me"* x>0 (i) Ect out an algorithm for sampling from A(x) using the inverse transform method. [3] Now also consider the following density function, the "half-normal" distribution: ,x30 OVI Let M be the maximum of f(x) hix) (ii) Show that M = . [2] (iii) Set out an acceptance-rejection algorithm, using A(x), which generates samples from the half normal distribution /(x). 137 (iv) Determine the value of 2. for which the algorithm is the most efficient fie. on average require fewest samples from h(x) to generate samples from /(x)). [3] (V) Show that the samples from part (ili) can be used to generate samples from the normal distribution with mean p and variance o. [3] [Total 14]