ACTSC232 Lecture Notes - Probability Distribution, Rate Function, Actuarial Science

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Summary of lecture notes - actsc 232, winter 2010. Part 1 - survival distributions and life tables. 1. 1 future lifetime random variables (a) let (x) denote a life or person aged x( 0) at time 0 or at the current time. (b) let tx denote the time-until-death of (x). That is to say that (x) will die at age x + tx or will die in tx years or tx is the death time of (x). The random variable tx is called the future lifetime of a life (x). Note that tx > 0 is a continuous random variable. (c) the distribution function (d. f. ) of tx is denoted by. Fx(t) = pr{tx t}, t 0. The survival distribution (s. f. ) of tx is denoted by. Sx(t) = pr{tx > t} = 1 fx(t), t 0. The probability density function (p. d. f. ) of tx is denoted by fx(t) = d dx. Note that t0 > 0 is a continuous random variable.

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