Assignment8: Problem 17 (1 point) Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The probability density function giving the distribution of t is p(t) = Cert for some positive constant C, and the cumulative distribution function is F(t) = So p(x) dx. Think carefully about what the practical meaning of F(t) is, being sure that you can put it into words. (a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). S(t) = e^(-Ct) (b) Suppose that a patient has a 80 percent chance of surviving at least 3 years. Find C. C = -1/3(In(0.8)) (c) Using the value of C you found in (b), find each of the following: the probability that the patient survives up to (that is, less than or equal to) 2 years: (-e^(-2*(-1/3(In8))+1