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A pair of random variables has a joint PDF specified by
fX,Y(x,y) = dexp(-(ax2+bxy+cy2)).
(a) Find the constant in terms of ,a , b and c . Also, find any restrictions needed for a , b and c themselves for this to be a valid PDF.
(b) Find the marginal PDFs fX(x) and fY(y).
(c) Find Pr(X>Y) .
For each of the F statistics given above find the degrees of freedom and an approximate P-value. Summarize the results of these tests.
Suppose you perform a hypothesis test relating to environmental toxins in a thriving small city in West Virginia. Discuss the risk to all interested parties in the scenario if you make a Type I error and if you make a Type II error
when 12 bolts are tested for hardness their indexes have a standard deviation of 41.7. test the claim that the standard
A random sample of 100 voters found that 44% were goint to vote for a certain candidate. Find the 99% limit for the population proportion of voters who will vote for that candidate.
use the normal distribution of sat critical reading scores for which the mean is 500 and the standard deviation is 108
A company sells two products (Product 1 and Product 2) that tend to be substitutes for each other. That is, if a customer buys Product 1, she tends to not buy Product 2, and vice versa.
The definition of a probability model. Illustrate the two parts of the definition with an example selected from the worksheet.
Think about how correlation is often miscast as causation. That is, cause is attributed to a variable when in fact.
What is the probability that the oven will cause a core to be defective? What is the probability that the temperature of the oven will range from 460 degree F to 470 degrees F?
for quality control purposes a company that manufactures copper sheets routinely takes samples from its production
To cross a single lane of moving traffic, we require at least a duration d. Successive car interarrival times are independently and identically distributed with probability density function fT (t).
The National Center for Health Statistics indicate that 29.9% of a sample of men and 0.5% of a sample of women are 6" or taller. Are these results generally consistent with your calculations?
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