3-5.1 A random variable X has a probability density function of fx(x) = 2x 0 x 1 = 0 elsewhere and an independent random variable Y is uniformly distributed between -1.0 and 1.0. a) Find the probability density function of the random variable Z = X +2Y. b) Find the probability that 0 < Z 1. 4 Question IV: You are given that the stochastic process for a stock is described by: dS = dt + odz S If there is a financial instrument of value V where V = Se-t/10, determine the process that V follows. Provide your answer in the form dVaVdtbv dz where a and b will contain the parameters and . If you are given that "a" in the process for V is equal to 3%, and = 1%, what is the volatility of S? 2. A random variable is normally distributed with a mean of u 50 and a standard deviation of = 5. a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. b. What is the probability that the random variable will assume a value between 45 and 55? Empirical Rule. c. What is the probability that the random variable will assume a value between 40 and 60? Empirical Rule. d. What is the probability that the random variable will assume a value between 35 and 65? Empirical Rule. e. What is the probability that the random variable will assume a value 60 or more? f. What is the probability that the random variable will assume a value between 40 and 55? g. What is the probability that the random variable will assume a value between 35 and 40?