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Let X denote the lifetime of a component, with f (x) and F(x) the pdf and cdf of X. The probability that the component fails in the interval (x, x + ?x) is approximately f(x) ? ?x. The conditional probability that it fails in (x, x + ?x) given that it has lasted at least x is f(x) ? ?x/[1 F(x)]. Dividing this by ?x produces the
An increasing failure rate function indicates that older components are increasingly likely to wear out, whereas a decreasing failure rate is evidence of increasing reliability with age. In practice, a "bathtub-shaped" failure is often assumed.
a. If X is exponentially distributed, what is r(x)?
b. If X has a Weibull distribution with parameters a and b, what is r(x)? For what parameter values will r(x) be increasing? For what parameter values will r(x) decrease with x?
so that if a component lasts b hours, it will last forever (while seemingly unreasonable, this model can be used to study just "initial wearout"). What are the cdf and pdf of X?
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To find the probability that exactly 25 of the computers will require repair, one would use what type of probability distribution?
A clinical study was performed to determine if a product was effective in alleviating side effects caused by a mode of treatment. In the treated group (100 subjects) it was found that 10% had side effect A, 15% had side effect B and 65% had side eff..
question an independent golf equipment testing facility compared the difference in the performance of golf balls hit
Consider the following exponential probability density function: This number represents the time between arrivals of customers at the drive-up window of a bank.
a safety light is designed so that the times between flashes are normally distributed with a mean of 4.50 s and a
calculate the samplenbspcovariancenbspbetween two variables x and y using the formulas described in lecture or
Use the normal approximation to find the probability that the student scores 70% or lower on a 100-question test.
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