4. The amount of time T (in hours) that a certain electrical component takes to fail...
4. The amount of time T (in hours) that a certain electrical
component takes to fail has an exponential distribution with
parameter 
(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
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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...
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.
Example 1: Electronic components of a certain type have a length life (in hours) X, that...
Example 1: Electronic components of a certain type have a length life (in hours) X, that follows the exponential distribution with probability density given by f(x) = (1/100)e ^ [(− 1/100)x] , x > 0. a. Suppose that 2 such components operate independently and in series in a certain system (that is, the system fails when either component fails). Find the density function for the length of life of the system. b. Suppose that 2 such components operate independently and...
5. (15 Points) Let T be a random variable that is the time to failure (in...
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...
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 r...
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 seriesas shown:As soon as one...
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...
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...
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...
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...
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...
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...
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