Let 0 S c S l (c is a number) and f: (x) and 1512:) be two continuous probability density functions (PDF) with associated cumulative distribution functions (CDF) F 1 (x) and Fx} and survival functions 3 1(x) = 1- F100 and 3:00 = l _ F200, respectively. Let g(x) = c f1 (x) + {1 ~ 0f; (x). Please answer the following questions. 1. Show that 3(x) is a valid density function. 2. Write the CDF associated with 30) in terms of F 1 (x) and F28). 3. Write the survival function (that is, one minus the CDF) associated with 3(x) in terms of Slur) and S 20')