Q2. (8 points) Newbie Insurance Company has just launched its first insurance product for retired people. As a starting point, they've decided to use the LTAM Standard Ultimate Life table. As a new hire, you're tasked to evaluate manage and update the survival model. a) For starters, you are considering including a fractional age assumption between integer ages. You examine a particular case of people aged 65.5 years who survive beyond the age of 90. What is the probability value of this case using UDD between integer ages? b) Also examining the particular case of people aged 65.5 years who survive beyond the age of 90, what is the probability value of this case using constant force of mortality between integer ages? c) You explore using a generalized de Moivre's law model. You set w = 120 and k = 10,000. What value of a should be such that 965 from the LTAM Standard Ultimate Life table matches 965 using the generalized de Moivre's law model? d) After six months, and gathering data, you believe that a generalized de Moivre's law model with w = 120, k = 10,000, and a = 0.5 to be a good fit. The company would like some key statistics, namely the range of values the model will typically produce before implementing it. For a 65-year-old, what would be their 1 percentile and 99 percentile remainder lifetime values?