The random variable X measures the lifetime of a (random) light bulb and is Weibull distributed with cumulative distribution function Fx (x) = 1 - e-x (for x 0). a. This lamp is subject to wear and tear. Express this mathematically. b. Prove that the lamp is subject to wear and tear. Clue: (t+s) t + s fort, s 0. c. Show that E[X] = /2 and Var[X] = 1 - /4. d. Approximate the probability that there is more than 95 hours of light if 100 such lamps burn in succession and independently of each other (each time until they break).