3. After graduating you've decided to start your own insurance company. You have already sold some policies. At the start of each month you receive $500 in premium payments. During each month you also have outgo though, in the form of claim payments that you have to make. Using your modelling skills from your degree, you have derived that your monthly outgo can be modelled by a Gamma(45, 0.1) distribution. You assume that these monthly outgoes are independent of each other. Now suppose that at the start of a year your company has $100 in its bank account. Using Monte Carlo simulations, determine the probability that at some point during the year your company will sadly run out of money. [4 marks] 4. While working through the exercises for this week with your friend, she says 'Have you noted that in all examples and exercises where we worked out the acceptance-rejection method, the value of c that we find is always greater than or equal to 1?'. You're of course very impressed by your sharp friend and start to think about this. Is it in the acceptance-rejection method always necessarily true that c > 1 or is it also possible that c E (0, 1)? Motivate your answer. [4 marks]