Answer Happy

Determine the mean and variance, if they exist, of its
associated random variable.
4.1 For each of the probability distribution functions (PDFs) given in Problem 3.1 (Page 67), determine the mean and variance, if they exist, of its associated random variable. (a) Case 1: [0, for x < 5; F(x) a, for x ≥ 5. (b) Case 2: for x < 5; F(x)= for 5 < x <7; for x 27. (c) Case 3: 0, for x < 1; 1/a, for k<x<k+1, and k = 1,2,3..... J=1 (d) Case 4: [0, for x ≤ 0; F(x)= = 1-e, for x>0. (e) Case 5: 0. for x < 0; F(x)= , for 0≤x≤1; 1, for x> 1. (f) Case 6: 0, for x < 0; F(x)= asin¹ √√x, for 0≤x≤ 1; 1. for x > 0. (g) Case 7: for x < 0; F(x) x) = {a(1-6-1/2) {a(1-e-x/2) + for x ≥ 0. F(x) = = = = 0, 1 3 a,