4. The amount of time T (in hours) that a certain electrical component takes to fail has an exponential distribution with parameter > 0. The component is found to be working at midnight on a certain day. Let N be the number of full days after this time before the component fails (so if the component fails before midnight the next day, N = 0).
(a) What is the probability that the component lasts at least 24 hours?
(b) Find the probability mass function of N.
c) Identify the distribution of N by name.
d) Given that the component is found to have failed on a certain day, what is the distribution function of the number of hours H past midnight that the component failed? 7 marks
4. The amount of time T (in hours) that a certain electrical component takes to fail...
The probability density function of the time to failure of an electronic component in a copier (in hours) is for . Determine the probability that a) A component lasts more than 3000 hours before failure. b) A component fails in the interval from 1000 to 2000 hours. c) A component fails before 1000 hours. d) Determine the number of hours at which 10% of all components have failed.
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function f(x,A) =e, if >0 10, otherwise. Compute the probability that a given component will fail in 5 years or less. 5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function...
An electronic component is randomly drawn from a sampled lot. This type of fails in accordance with a Weibull distribution having a shape parameter -1.5 and a scale parameter η 100 hours, what is the probability that the item fails before achieving a lif x-25 months? (b) e of (9 marks) An electronic component is randomly drawn from a sampled lot. This type of fails in accordance with a Weibull distribution having a shape parameter -1.5 and a scale parameter...
The time in hours during which an electrical generator is operational is a random variable with rate 1/160. a) Determine both pmfipdf and cdf of X-time in hours during which an electrical generator is operational. b) What is the probability that the generator will be operational for more than 40 hours? c What is the probability that the generator will be operational between 60 and 160 hours? d) Suppose that 5 generators are obtained and at least 3 working generators...
A system consists of five identical components connected in series as shown:As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with ? = 0.01 and that components fail independently of one another. Define eventsAi= {ith component lasts at least t hours}, i = 1, . . . , 5, so that the Ais are independent events. Let X = the time at which the system failsthat is, the...
5. For a certain machine it can be assumed that the probability that it fails in any given hour is approx- imately .0002 (we assume that this probability does not change during the life time of the machine). An hour being a sufficiently short time, we may assume that the lifetime X of the machine follows the exponential distribution with parameter 1 = .0002, where time is measured in hours. (In the notation of the textbook, this is the distribution...
4. Reliability of Systems - Take n components to have failure times Ti, T2, ..., Tn If we construct a complex system out of these distribution of the failure time T of the entire svstem in terms of the distributions of Ti, T2, ..., Tn. There are two basic networks. In a series hookup, the system fails as soon as any one of the components fails. Hence T - min(T1, T2, ...,Tn). In a parallel hookup the system is operational...
Example 7 The amount of electricity (in hundreds of kilowatt-hours) that a certain power company is able to sell in a day is found to be a random variable with the following probability density function (pdf): kx k(10-x): 0: 0sxs5 5 x 10 elsewhere n) = (i) (ii) Find the value of k. What is the probability that the amount of electricity that will be sold is more than 600 kilowatt-hours. (ii) What is the probability that the amount of...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
A juicer works for T amount of time before it breaks, where T follows the exponential distribution with rate = 3. After sales service examines the juicer at times distributed according to a Poisson process with rate = 2; if the juicer is found to be not working then it is immediately substituted. 1) Find the probability that a juicer is examined at least 2 times before it stops working. 2) Find the expected time between replacements of juicers. We...