ISYE 330 Chapter 4 Exercises 4.1.5 Suppose that f(x) = 1.5x² for −1 < x < 1. Determine the following: a) P(0<X) b) P(0.5<X) c) P(-0.5 ≤x≤ 0.5) d) P(X<-2) e) P(X<0 or X > -0.5) 4.2.1 Determine the following: a) P(X<2.8) b) P(X>1.5) c) P(X<-2) d) P(X>6) F(x) = 0.25x 1 0.2 X x < 0 0≤x < 5 5 ≤ x/n 4-98) The time between the arrival of electronic messages at your computer is exponentially distributed with a mean of two hours. (a) What is the probability that you do not receive a message during a two-hour period? (b) If you have not had a message in the last four hours, what is the probability that you do not receive a message in the next two hours? (c) What is the expected time between your fifth and sixth messages?/n 1. 2. Chapter 4: Exercises Use Appendix Table III to determine the following probabilities for the standard normal random variable Z: (a) P(Z < 1.32) (b) P(Z < 3.0) (c) P(Z > 1.45) (d) P(Z >-2.15) (e) P(-2.34 <Z<1.76) The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a standard deviation of 600 hours. (a) What is the probability that a laser fails before 5000 hours? (b) What is the life in hours that 95% of the lasers exceed? (c) If three lasers are used in a product and they are assumed to fail independently, what is the probability that all three are still operating after 7000 hours?