The operating lifetime of an electronic component is known to have a normal distribution with mean...
The operating lifetime of an electronic component is known to have a normal distribution with mean of 2,500 hours and variance of 40,000 (hours^2). Given that the component has been operating for 2,350 hours, what is the probability that it will still be operating beyond 2,750 hours?
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The operating lifetime of an electronic component is known to have a normal distribution with mean...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2)...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
The usable lifetime of a particular electronic component is known to follow an exponential distribution with...
The usable lifetime of a particular electronic component is known to follow an exponential distribution with a mean of 6.6 years. Let X = the usable lifetime of a randomly selected component. (a) The proportion of these components that have a usable lifetime between 5.9 and 8.1 years is . (b) The probability that a randomly selected component will have a usable life more than 7.5 years is . (c) The variance of X is
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by That is, Y has a gamma distribution with parameters α = 2 and θ. Let denote the MLE of θ. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of θ. b Find E() and V(). c Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What...
Plz use MGF technique The lifetime of an electronic component in an HDTV is a random...
Plz use MGF technique
The lifetime of an electronic component in an HDTV is a random variable that can be modeled by the exponential distribution with a mean lifetime ß. Two components, X1 and X2, are randomly chosen and operated until failure. At that point, the lifetime of each component is observed. The mean lifetime of these two components is X1 + X2 X =- a) Find the probability density function of x using the MGF technique (the method of...
a certain brand of batteries has a lifetime with a normal distribution, a mean of 3750...
a certain brand of batteries has a lifetime with a normal distribution, a mean of 3750 hours, and a standard of 300 hours. what is the probability that the batteries will last between 3800 and 4100 hours. round to 4 decimal.
Let X be the lifetime of an electronic device. It is known that the average lifetime...
Let X be the lifetime of an electronic device. It is known that the average lifetime of the device is 747 days and the standard deviation is 108 days. Let be the sample mean of the lifetimes of 164 devices. The distribution of X is unknown, however, the distribution of a should be approximately normal according to the Central Limit Theorem. Calculate the following probabilities using the normal approximation (a) Pa s 737) (c) P(737 i 763): Check
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of ea...
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of each component follows an exponential distribution with a mean lifetime of 2 years. Determine the probability the machine is still operating after 1.5 years. Suppose the machine in the previous problem requires all three of the components to operate. If the lifetime of each component follows...
Please show all steps. The lifetime of an electronic device has a normal distribution with standard...
Please show all steps.
The lifetime of an electronic device has a normal distribution with standard deviation 1.5 years. A random sample of 400 devices was drawn yielding the sample lifetime average of 6 years. a) Compute a 95% confidence interval for the mean lifetime of the electronic devices.
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
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 lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
Plz use MGF technique
The lifetime of an electronic component in an HDTV is a random variable that can be modeled by the exponential distribution with a mean lifetime ß. Two components, X1 and X2, are randomly chosen and operated until failure. At that point, the lifetime of each component is observed. The mean lifetime of these two components is X1 + X2 X =- a) Find the probability density function of x using the MGF technique (the method of...
Let X be the lifetime of an electronic device. It is known that the average lifetime of the device is 747 days and the standard deviation is 108 days. Let be the sample mean of the lifetimes of 164 devices. The distribution of X is unknown, however, the distribution of a should be approximately normal according to the Central Limit Theorem. Calculate the following probabilities using the normal approximation (a) Pa s 737) (c) P(737 i 763): Check
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of each component follows an exponential distribution with a mean lifetime of 2 years. Determine the probability the machine is still operating after 1.5 years. Suppose the machine in the previous problem requires all three of the components to operate. If the lifetime of each component follows...
Please show all steps.
The lifetime of an electronic device has a normal distribution with standard deviation 1.5 years. A random sample of 400 devices was drawn yielding the sample lifetime average of 6 years. a) Compute a 95% confidence interval for the mean lifetime of the electronic devices.
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
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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