The random variable X measures the lifetime of a (random) light bulb and is Weibull distributed...

 

Transcribed Image Text:

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). 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).

Answer rating: 100% (QA)

a Mathematically the lamp being subject to wear and tear means that its lifetime is influenced by ex... View the full answer