If fx₁x₂ (x₁, x₂) is a joint density function, then find the joint density function of Y, and Y₂
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A: The PDF of X and Y is given as:Also, the given transformation is:U=5XYandV=8X
![If ƒx₁x₂ (x₁, x₂) is a joint density function, then find the joint density function of Y, and Y₂](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F069954e9-8e41-4d3d-9c00-ce7a61c02c03%2F088a08b5-4057-428b-a7df-a71a6eaabff6%2Fkvhhmek_processed.jpeg&w=3840&q=75)
![Let two random variables Y, and Y₂ be linear transformations of X₁ and X₂ given by
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Y₁ = X₁ + X₂
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Y₂ = 2X₁ +3X₂
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- Suppose that X and Y have a joint probability density 7e-2-7y if x, y ≥ 0 otherwise (a) Verify that fx.y is indeed a probability density function. function given by fx.x (x, y)We determined that f(y,, Y2) [6(1 - Y2), 0s Y, SY2$ 1, elsewhere, is a valid joint probability density function.Let X and Y have joint density function fxy (x, y) = x + y for 0Find the Moment Generating function for the density function in the attached file. f(x) = x-1, a> 0, x 20 מיגLet X, Y have the joint density function 2 \exp(-x-y) if Are they independent? Find Cov(X,Y). 0"Medians, etc problem." Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman