The useful life of electrical circuits produced by your company has a uniform distribution defend by the probability density function:

where x = values for the random variable “useful circuit life in hours” 

a. Determine the probability that useful circuit life will be between 1060 and 1085 hours. 

b. Determine the probability that useful circuit life will be at least 1020 hours. 

c. Determine the mean (expected value), the variance, and the standard deviation of the “useful circuit life” random variable. 

d. Show that the total area associated with the probability density function here is 1.0. That is, demonstrate that P(1000 ≤ x ≤ 1100) = 1.0. Explain the significance of this property.

Transcribed Image Text:

1/10 for x values between 1000 and f(x) 1100 hours lo everywhere else