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- Let W₁ < W₂ < ... < Wn be the order statistics of n independent observations from a U(0, 1) distribution. (a) Find the pdf of W₁ and that of Wn. (b) Use the results of (a) to verify that E (W₁) = 1/(n+1) and E(Wn) = n/(n+1).Calculate the residual of P = (1.2, 2.4) with respect to the line 3x + 4y = 12.Suppose Y, and Y, are random variables with joint pdf fy,x, (V1,Y2) = S6(1 – y2), 0, 0 < y1 < y2 otherwise Let U1 =4 and U2 = Y,. Use the transformation technique to show that Ui follows a uniform %3D distribution from 0 to 1.
- J 2Consider the joint pdf fxy(x, y) = cxy, for 0X is a random variable that has the following PDF function: fx(x) = 0.28(x + 2) + 0.38(x + 1) + 0.358(x) + 0.158(x – 1) %3D For y = x2, find: 1- fy) 2- Fy(y) 3- E[y] 4- o1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.Let X and Y be two independent random variables with PDFS fy (x) = 1536 x4 with x> 8 and fy(y)= 25 Y with 012. Let the random variable X and Y have joint pdf 4 f(x,y) = (x² + 3y²), 0Recommended 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