Chapter 4, Problem 187SE

Refer to Exercise 4.186. Resistors used in the construction of an aircraft guidance system have life lengths that follow a Weibull distribution with m = 2 and α = 10 (with measurements in thousands of hours).

1. a Find the probability that the life length of a randomly selected resistor of this type exceeds 5000 hours.
2. b If three resistors of this type are operating independently, find the probability that exactly one of the three will burn out prior to 5000 hours of use.

^*4.186    The random variable Y, with a density function given by

$f(y)=\frac{m{y}^{m-1}}{\alpha }{e}^{-y^m/\alpha },0\le y<\infty ,\alpha ,m>0$

is said to have a Weibull distribution. The Weibull density function provides a good model for the distribution of length of life for many mechanical devices and biological plants and animals. Find the mean and variance for a Weibull distributed random variable with m = 2.