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"I have two batteries of different brands. Each has a lifetime defined by an independent random variable. The PDF of each follows
Brand A : fX(x) = { e^-x, if x>=0 and 0 otherwiseBrand B : fX(x) = { 3e^(-3x), if x>=0 and 0 otherwise
Both battery brands are tested side by side, starting at t = 0. As each battery runs out, it is instantly replaced.
1) What is the expected number of brand B failures until a given time t?
2) What is the PDF of the amount of time before the first failure of either battery brand?
3) What is the expected value of the time until the third Brand B battery fails? What is the variance of that time?
4) Given that a Brand A battery just failed, what is the expected value of the time we wait until the next Brand B failure?"
A jar contains 2 black marbles and 8 white marbles. If you randomly pick 2 marbles without replacement, what is the probability that you get one marble of each color?
A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a standard deviation of 3.9 percent. The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a stan..
Suppose that 10 years ago the average annual expense for stock funds was 1.19 percent. Let µ be the current mean annual expense for all stock funds, and assume that stock fund annual expenses are approximately normally distributed.
The normal distribution has several characteristics that make it the underlying foundation of much of inferential statistical tools.
You've two separate sets of data. From one set you calculate the standard error to be 500. From the other set, the standard error was 5.
Determine whether each of the distributions given below represents a probability distribution. Justify your answer.
Estimating a linear regression equation to predict the future values of the dependent variable Y.
Costs of Televisions Listed below are prices (in dollars) and quality rating scores of rare-projection televisions (based on data from Consumer Reports). All of the televisions have screen sizes of 55 in or 56 in.
An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that 10-mg dose of the drug is lethal 5% of the time within the first 4 hours; of the animals alive at 4 hours, 10% will die in the next 4 hours..
A deck of 52 cards is dealt face up in a row. What is the probability that all 4 aces and all 4 kings are adjacent (but in any order)?
Developing the histogram and pie chart for the sample data.
lowering the price does not decrease this behavior and we should not decide to lower prices based on this research." Comment on the executive's conclusion. What type of inference is being made? Will the decision not to lower prices be a good one.
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