5. (Sec. 5.1) Suppose the marginal pdfs of two independent rvs X and Y are given by 5x4 for 0 |0 otherwise 1 fx(r) 2y3for 0y <1 |0 otherwise fy(y) (a) Find the joint pdf of X and Y (b) What is the probability that both X and Y are greater than .5? (c) What is the probability that at least one of X or Y is greater than .5?
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- The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650 0.255 0.147 0.855 0.174Question 2 Let joint pdf for X and Y as follow: f (x, y) = *(2-y) 4 for 0Which of the following is the correct sum of squared residuals to be minimized to find tne fit f(x) = £ (2r-1)"* - using a data set ((xo, Yo), (x1,y1), --, CKn. Yn)} ? A.) Eo(In(y;) + a – b2x; + 1)² B.) E-(In(y;) + In a + b In(2x; – 1))² D.) E7-o(In(y;) – In a – b In(2x; – 1))² E.) E-o(In(y;) + In a – b2x; + 1)²7.If X is a continuous RV whose PDF is given by Find c.and mean of X. _[c(4x-2x²), 0EL 466 416 13.) The continuous random variable (RV) X is uniform over [0,1). Given Y = -ln X what is P({0fx₁x (x₁y) = х-у 2e-x-y if x 71 9710 {26-23 2⁰ } otherwise J Find fycy) and fx cx) where fxiy (xiy) is joint pdf and fycy) / fx(x) are marginal distribution functions -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