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You own a store that sells light bulbs. Customers have been complaining that the bulbs you sell burn out quickly. You want to identify which of two factories (Factory A or Factory B) is the one producing the current batch of light bulbs in your store. You have n light bulbs in your test batch, but you do not know from which factory these bulbs came. Furthermore, you have no a priori reason to think one factory is more likely than the other. You have examined m light bulbs (where m < n) and you have measured the lifetime of these m light bulbs.
Assume that the light bulbs produced in Factory A have a lifetime you can model as being exponentially distributed with parameter A. Assume that the light bulbs produced in Factory B have a lifetime you can model as being exponentially distributed with parameter B. Finally, assume that the lifetimes of the light bulbs are conditionally independent given the parameters.Let be the exponential failure rate for light bulbs in your test batch of size n.(a) Assuming that you know A and B, write the posterior probability distribution of .(b) Assume the following independent prior distributions for A and B:AjA; A Gamma(A; A)BjB; B Gamma(B; B)The posterior distribution of with these assumptions. What is the name of this type of distribution?
Company wishes to know how many pounds of each chemical ingredient to put into the bag of fertilizer to meet minimum needs of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium during minimizing cost.
If the gender-selection method has no effect and boys and girls are equally likely, find the mean number of boys born in groups of 152. Round to the nearest whole number.
What would be your best point estimate for average Sales in weeks for which Newspaper advertising were $1 million? What would be an appropriate interval estimate for this?
Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
Elucidate correlation coefficient of determination R-square also Adjusted R-square. A computer utility was implimentated to the data collected in a study of a generalized health.
Subscribe to Cool Teen and 35% subscribe to neither magazine, what is the probability that a randomly selected teenager subscribes to both magazines?
Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the hospital is single or has a college degree is?
Why might supposition of normal population be doubtful? Problem arises when?
The number of shark attacks and deaths over a recent 5- year period is shown. Find the mean, median, mode, midrange, variance, and standard deviation for the date. Which data set is more valuable?
On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall below a score of 83.8?
Describe the sampling distribution of p-hat, the sample proportion of college students with the cell phones who send or receive the text messages with their phones.
A large population of overdue bills has balances that follow a normal curve. When we take a sample of 100 of these the average is $500 and the SD is $100.
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