2. For each of the following, show whether or not it is a survival function. 2 a. Sx(t) = t+2 2 1+ b. Sx(t) t+2 = 2 c. Sx(t) = (1 t)et d. Sx(t)=(1+t)e-t Which represent valid survival functions? Sx(t) = e0.01t 1 Sx(0) = 1 - 0.01t t 100 0 t > 100 2 lim Sx(t) = 0 t 3 non increasing function Sx(t) {1 XX Sx(t) = cos(t) Sx(t) = Sx(t) = = 50 t t 50 t > 50 0 x+1 x+1+t Violates conditions 2 & 3 Violates condition 1 4. You are given the following life table: lx 100 100 101 90 102 76 103 58 104 40 105 25 106 12 107 0 Calculate: a) The curtate life expectancy for a 100-year-old (E100). b) An approximation for the complete future life expectancy for a 100-year-old.