49. If the distribution of the random variable (x, y) is defined by the density f (x, y) = • [1+xy (x - y) ] for lxl < 1, lyl < 1 | =0 elsewhere show that x and y are not independent.
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![49.
If the distribution of íhe random variable (x, y) is defined by
the density
f (x, y) = { [1 + xy (x² – y²) ] for lxl < 1, lyls 1
||
4
=0 elsewhere
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show that x and y are not independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb007501-3105-4092-9424-569223a9ca16%2F5a5a1f5a-db6e-4613-9f8e-be70c85e60c0%2Fe5l5fn8_processed.jpeg&w=3840&q=75)
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- Suppose (X, Y) is a joint continuous random variable with joint density function, f(x, y) = {cxy, for 1Y other words find theThe continuous random variables X and Y are statistically independent and have marginal density functions fx(x) = 2x, 0 1. y2' Calculate the probability P(X < 0.5, Y < 2)4. Let X and Y be independent, continuous random variables with densities and fx(x) = = fy (y) = = 0 {} if 0 < x < 2 otherwise. y if 0Suppose that the amount of time a hospital patient must wait for a nurse's help is described by a continuous random variable with density function f(t) = e-t/3 where t≥ 0 is measured in minutes. (a) What is the probability that a patient must wait for more than 4 minutes? (b) A patient spends a week in the hospital and requests nurse assistance once each day. What is the probability that the nurse will take longer than 5 minutes to respond on (exactly) two occasions? (c) What is the probability that on at least one call out of seven, the nurse will take longer than 7 minutes to respond?Please Answer AsapExz fet X, X2, Xn fat X, Xz, be a random dist ribution witk sample from Hhe 'parameter A Paissen Estimate 1.Let the random variable X have'the marginal density 1 f, (x)= 1, 125. Let X and Y be continuous random variables with joint density function for 0Please integrate for both x yRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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