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Suppose that X and Y have a joint probability density function (pdf)
f(x; y) =
k(x + 2y) for 0 < x < 1 and 0 < y < 1;
0 otherwise.
(a) Find k such that f(x; y) is indeed a valid pdf.
(b) Find the marginal pdf of Y .
(c) Find E(Y ).
(d) Find the conditional pdf fXjY (x j y).
(e) Find P(X 0:5 j Y = 0:5).
the following data represent the costs in dollars of a sample of 30 postal mailings by a
The heights of young women are approximately normal with mean 65 inches and standard deviation 2.5 inches.
According to Chebyshev's Theorem, how many students scored between 57 and 93? Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 57 and 93?
What is a hypothesis? Specifically, is it a statement about the population or the sample? What is the purpose of hypothesis testing?
Quality Progress, February 2005, reports on improvements in customer satisfaction and loyalty made by Bank of America. A key measure of customer satisfaction is the response (on a scale from 1 to 10) to the question
Given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?
Given that the safety conditions at the plant remain the same next year, what is the probability that the number of serious injuries will be less than 2?
The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution.
discuss the physical emotional cognitive and behavioural responses an individual is likely to experience in response to
One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?
We want to estimate the delay using the correlation analysis. Determine analytically the autocorrelation ryy(l) in terms of the autocorrelation rxx(l).
The mean weight of newborn babies in a Long Island Community is 7.5 lbs with a standard deviation of 1.4 lbs. What is the probability that a random sample of 49 babies has a sample mean weight of at least 7.2lbs?
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