A ten-year term insurance is be issued to a life aged 50. The sum insured is $200,000 and payable immediately upon death. Premium payments are annual in advance. a) Using the SOA Standard Ultimate Life Table at i = 5% and UDD, compute the net annual premium determined by the equivalence principle. b) Find the probability that this contract makes a profit. c) Compute the gross premium determined by the equivalence principle if the initial expense is $500 plus 10% of the first premium, and if there is a renewal expense of 2% of the annual premium payment for the second and all subsequent premium payments.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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