A factory manufactures electronic control units. The probability that a control unit has an error is...
A factory manufactures electronic control units. The probability that a control unit has an error is 8%. All devices are tested before use, but the test does not always give the correct answer. We say that the test fails if the test indicates that the device has an error. If a device really has a fault, the probability is 88% that the test will fail. If a device is flawless, there is a 95% probability that the test will not fail. Only devices that do not turn off the test will be used. Let D be the event that a device has an error and let T be the event that the test fails. a) From the information given above, write down what P (D), P (T | D) and P (T | D) are. Calculate P (D) and P (T | D). What is the probability that the test turns on a random unit, P (T)? What is the probability that a device being used has an error?
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A factory manufactures electronic control units. The probability
that a control unit has an error is...
A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites....
A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites. The control devices are shipped by truck to customers' sites; while in transit, the devices sometimes get out of alignment. More specifically, a device has a prior probability of .10 of getting out of alignment during shipment. When a control device is delivered to the customer's plant site, the customer can install the device. If the customer installs the device, and if the device...
A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites....
A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites. The control devices are shipped by truck to customers' sites; while in transit, the devices sometimes get out of alignment. More specifically, a device has a prior probability of 10 of getting out of alignment during shipment. When a control device is delivered to the customer's plant site, the customer can install the device. If the customer installs the device, and if the device...
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...
has tested positive for a disease and wants to know the probability she actually is sick...
has tested positive for a disease and wants to know the probability she actually is sick given the positive test. The test has a sensitivity and specificity of 95%, but the prevalence is only 1/1000. Let A test positive and B the event Alicia has the disease. a) Write each of the figures above in proper notation. the event Alicia h@y p://ame b) Create a hypothetical two-way table to represent this situation. fooo a 5000 Hr do o Create a...
A electronics manufacturer has developed a new type of remote control button that is designed to...
A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 29 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of x¯x¯ = 1261.3 hours and a sample standard deviation of s = 119.4. Independent tests reveal that the mean lifetime of the...
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...
(8 points) A electronics manufacturer has developed a new type of remote control button that is designed to operate lon...
(8 points) A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 26 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of x = 1255 hours and a sample standard deviation of S = 112.3. Independent tests reveal that the mean lifetime...
3119A (Read-Cnly] Word The breaking strength of a fabric types A and B has been tested 4 times and found A 4.2,4.5, 3.8, 5.3 psi. B 53, 56, 60, 6.0 (A competing new fabric) Test the claim saying...
3119A (Read-Cnly] Word The breaking strength of a fabric types A and B has been tested 4 times and found A 4.2,4.5, 3.8, 5.3 psi. B 53, 56, 60, 6.0 (A competing new fabric) Test the claim saying average strength must be the same. Use X values with Cl, use Z/t values and use p values. State the conclusion with p values. Show calculations Answer! Question 4. A random experiment can result in one of the outcomes (a, b, c,...
QUESTION 8 [NOTE: The next 8 questions are all different parts of this question]. Before they...
QUESTION 8 [NOTE: The next 8 questions are all different parts of this question]. Before they can be marketed, all new medical devices must be approved by the Food and Drug Administration (FDA). A new device has a protective cover which needs to be removed easily. A similar device, already on the market, has a cover that requires an average force of 8 pounds to remove. The laboratory test data on a random sample of 9 of the new device...
Hi, my answers seemed strange after using Bayes theorem, so I am unsure if I made the right calcu...
hi, my answers seemed strange after using Bayes theorem, so I am
unsure if I made the right calculations. Please show your work so I
can catch my error :)
Extra Credit: ELISA tests are used to screen donated blood for the presence of the AIDS virus. The test actually detects antibodies, substances that the body produces when the virus is present. When antibodies are present, ELISA is positive with probability about 0.997 and negative with probability about 0.003. When...
A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites. The control devices are shipped by truck to customers' sites; while in transit, the devices sometimes get out of alignment. More specifically, a device has a prior probability of .10 of getting out of alignment during shipment. When a control device is delivered to the customer's plant site, the customer can install the device. If the customer installs the device, and if the device...
A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites. The control devices are shipped by truck to customers' sites; while in transit, the devices sometimes get out of alignment. More specifically, a device has a prior probability of 10 of getting out of alignment during shipment. When a control device is delivered to the customer's plant site, the customer can install the device. If the customer installs the device, and if the device...
has tested positive for a disease and wants to know the probability she actually is sick given the positive test. The test has a sensitivity and specificity of 95%, but the prevalence is only 1/1000. Let A test positive and B the event Alicia has the disease. a) Write each of the figures above in proper notation. the event Alicia h@y p://ame b) Create a hypothetical two-way table to represent this situation. fooo a 5000 Hr do o Create a...
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...
(8 points) A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 26 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of x = 1255 hours and a sample standard deviation of S = 112.3. Independent tests reveal that the mean lifetime...
3119A (Read-Cnly] Word The breaking strength of a fabric types A and B has been tested 4 times and found A 4.2,4.5, 3.8, 5.3 psi. B 53, 56, 60, 6.0 (A competing new fabric) Test the claim saying average strength must be the same. Use X values with Cl, use Z/t values and use p values. State the conclusion with p values. Show calculations Answer! Question 4. A random experiment can result in one of the outcomes (a, b, c,...
hi, my answers seemed strange after using Bayes theorem, so I am
unsure if I made the right calculations. Please show your work so I
can catch my error :)
Extra Credit: ELISA tests are used to screen donated blood for the presence of the AIDS virus. The test actually detects antibodies, substances that the body produces when the virus is present. When antibodies are present, ELISA is positive with probability about 0.997 and negative with probability about 0.003. When...
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