Let g(x) = cifi(x) + c2f2(x) + c3f3(x) where fi, f2, f3 are probability density functions with associated means and variances /1, 07, /2,07, M3,02. In other words, if a continuous random variable has density f; (j = 1,2, 3), the expectation of this random variable is ; and the variance of this random variable is o?. Here C1, C2, C3 E (0, 1) and c1 + C2 + c3 = 1. Please answer the following questions. 1. Show that g(x) is a valid probability density function. 2. What is the mean (expectation) associated with the probability density function g(x) as a function of C1, HI, C2, H2, C3, H3? 3. What is the variance associated with the probability density function g(x) as a function of C1, /1, 07, C2, H2, 02, C3, 13, 03