Problem 2) For the following random variable X. x<-3 0 0.4 Fx(x)= 0.8 [1 EXIDI -3≤x<5 5≤x<7 x27 a) Find the variance of the X. b) Find PX/B(x), where the condition B = {X>0}. c) Find E[XB]. DY
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- 7. a) Suppose that X is a uniform continuous random variable where 0Please state your assumptions and show all your work clearly. 1. Show that the following equalities hold: a) Population variance: N 'i=1 i=1 N N b) Sample variance: E,(xi – x)² E-,(x;)² n(x)? i=1 n – 1 n – 1 n – 1 c) Sum of differences from the population mean: Σα. > (xi – u) = 0 | i=14-52. If f(x) =e ,- coLet X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .41. Suppose that the PDF of X is given by 1+0.4x2 0< x <1 f(x) otherwise a. Find the expected value of X, E(X). b. Find the variance of X, Var(X). c. Find the standard deviation of X, Std(X)4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?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