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- Estimate the unknown parameter from a sample 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7 drawn from a discrete distribution with the probability mass functiontion 0 (P(3) P(7) = 1-0 0 - Compute the estimator of 0 use the method of moments.Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter 0 > 0 is defined by F(x; θ) - 1-el x > 0 i) What is the expected value of X,E(X)? ii) What is the variance of X,V(X)?Let X ~ Uniform(a, b). Find Expected value EX.
- Q2\ Consider is a continuous random variable with probability density function given by: Find: 1- P(50Find the expected value of the continuous random variable g(x)= x^2+3x+2, if the density function for random variable x are shown in the following equation. f() = [F(2x-1) 0Let X1, X2,...,X, be a random sample from a distribution with density function e if x > 0 f(x; 0) elsewhere What is the maximum likelihood estimator of 0 ?The joint PDF of two random variables X,Y is given byfXY(x, y) = {k e^(-y-x/4) , x > 0, y > 0 0, otherwisea) What is the value of k ?b) Find the probability P( X<Y ).c) Find P( 0<X<2 ).Suppose that the Cumulative distribution function (CDF) of the random variable X with parameter 0 > 0 is defined by F(x;0) = 1 - e , x > 0 i) What is the expected value of X,E(X)? ii) What is the variance of X,V (X)?Let X ~ N(0,o²) and Y ~ N(0, v²) be independent random variables and Z = X +Y. (a) Find the LMMSE estimator of X given Z. (b) Find the conditional distribution fzix(z, x).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