Suppose that the future lifetime of a newborn follows the survival function S0(t)=(105105t)1/3,for0t105. (i) Explain why this is a valid survival function. (ii) Calculate E(T0)=00 and interpret this value. (iii) Calculate 10q30 and interpret this value. (iv) Calculate the probability that (40) will die between ages 65 and 75. Suppose that the future lifetime of a newborn follows the survival function S0(t)=(105105t)1/3,for0t105. (i) Explain why this is a valid survival function. (ii) Calculate E(T0)=00 and interpret this value. (iii) Calculate 10q30 and interpret this value. (iv) Calculate the probability that (40) will die between ages 65 and 75