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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?
the administration at school is curious in determining the average gpa of its students. previous studies have shown
A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the popul..
assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of 2275
Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
as brian is leaving for college his parents give him a car but warn him that they would take the car away if he gets 6
Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project in order to minimize total cost. What is the total cost?
a traffic control engineer reports that. 75 of the vehicles passing through a checkpoint are from within the state.
The past history shows that 60% of employees prefer Starbucks brand coffee. A sample of 5 employees is selected, what is the probability that less than 3 prefer Starbucks?
Suppose that Total Revenue = 200Q and Total Cost = 80 + 50Q where Q, the quantity sold, is a random variable with expected value 20 and variance 4.
the mean gross annual incomes of certified welders are normally distributed with the mean of 20000 and a standard
given that z is a standard normal random variable compute the following probabilities to 4 decimals.a. pz -1.0b. pz
The weight of 500 american men were taken and the sample mean was found to be 194 pounds with a standard deviation of 11.2 pounds. what percentage of men have weights between 175 and 225 pounds
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