18.44 Lecture Notes - Lecture 29: Random Variable, Holda, Independent And Identically Distributed Random Variables
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One possibility: put the entire sum in government insured interest-bearing savings account. The (post-tax) interest rate equals the in ation rate, so the real value of his savings is guaranteed not to change. Riskier possibility: put sum in investment where every month real value goes up 15 percent with probability . 53 and down 15 percent with probability 0. 47 (independently of everything else). Pedro is considering two ways to invest his life savings. Computee[r ] = 0. 53 1. 15 + 0. 47 0. 85 = 1. 009. Answer: let r be i. i. d. random variables each equal to 1. 15 with probability 0. 53 and 0. 85 with probability 0. 47. Total value after n steps is initial investment times t := We wrote t = r r . Taking logs, we can write x = logr and s = logt = x. Now s is a sum of i. i. d. random variables. E[x ] = e[logr ] = 0. 53(log1. 15) + 0. 47(log0. 85) 0. 0023.
