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- The continuous random variable Y has the following pdf: 1- y?, 0Let X follow a uniform distribution with interval (0, 100] and Y be the excess loss random variable with d 25. Find the value-at-risk VAR0.95 (YP).(a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of X = (ii) If 1 = 0, name the distribution of X given in 3(a)(i).Consider X and Y are joint distributed with PDFf(x,y)=x+y, 0≤x≤1, 0≤y≤1. (d) Find the marginal distributions of X and Y .(e) Find the conditional distribution of X given Y = y.The joint distribution of X and Y is: Pxy(0,0)=1/10, Pxy(0,1)=a, Px,y(0,2)=2/10 Pxy(1,0)=a, Pxy(1,1)=b, Pxy(2,0)=2/10, Pxy(2,1)=a, Pxy(2,2)=1/10 Pxy(1,2)=a X,Y You want "a" to make the variance of Y as minimum as possible. The variance of Y equals. Select one: a. 1/2 b. 6/25 с. 2/5 d. 3/10 е. 3/5Given (x + 2y) ,03. Let X1,.., Xn be a random sample from a uniform distribution on the interval [a, b). In other words, X U(a, b). Obtain method of moments estimators for a and b.If Y = InX has a N (0, 1) distribution then E (X²) is equal toIn the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean λ = 3. The profit per foot when the rope is sold is given by X, where X = 60 - 4Y - y². Find the expected profit per foot. $ per foot1. 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.Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: The marginal function of X ,f1(X)(b) Consider the generalised three-parameter beta distribution with pdf 121?x (1 – x)² [1- (1 – 2) x]5* fx (x) = 0SEE MORE QUESTIONSRecommended 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