In a group of people of a given age (e.g. 65), some proportion of those people will not live another year. let qr represent the proportion of people of age x who will die before reaching age x + 1. The value qx is sometimes referred to as the mortality rate at age x. The following formula, based on Gompertz's Law, is sometimes used to model mortality. _ M q,,_1 EXPC Lilaqr) Assume the mortality rates for males at ages 63 and 64 are q63 = 0.0235 and (154 = 0.0262, respectively. And those of females at ages 63 and 64 are (153 = 0.0203 and q\" = 0.0225, respectively. Use simulation (>2000 trials) to answer the following questions. (20 pt) Questions: 1. On average, to what age should a 65yearold male expect to live? 2. What is the probability of a 65-year-old male living to at least age 80? 3. What is the probability of a 70-year-old female living to exactly age 80