Question

Page 5/6 Test#2 Name 15. The traveling time from office to the nearest airport owing probability mass function (PMF) shown in the figure. Please The mean, and the median, rom office is a discrete random variable and can be crmine the following information on the travel time: ) The skewness and skewn e skewnessnce, standard deviation and coefficient of variation, respectively: 3) vely o.30 0.25 0.20 o.10 0 10 0 05 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Tihours Figure for Problem 15: PMF of the travel time t

Answer 1

Mean (mu) = E(t) = Sigam^7_i = 1 ti p(ti) = 1(0) + (1.5) (0.05) + (2.0)(0.10) + (2.5)(0.3) + (3.0)(0.25) + (3.5)(0.2) + (4.0)(0.1) = 0.075 + 0.2 + 0.75 + 0.75 + 0.7 + 0.4 = 2.875 Therefore Mean (mu) = 2.875 hrs Median of a discrete random variable is the middle value It is the value of T for which p(T < t) is greater than or equal to 0.5 and p(T > t) is greater than or equal to 0.5 In this question median is t = 3 because p(T < 3) = p(t = 1) + p(1.5) + p(2.0) + p(2.5) + p(3) = 0 + 0.05 + 0.10 + 0.30 + 0.15 Rightarrow p(T < 3) = 0.70 p (T > 3) = p(t = 3) + p(t = 3.5) + p(t - 4.0) = 0.25 + 0.20 + 0.10 p(T > 3) = 0.55