Let X,, X2,... ,X, be a random sample from a distribution with density function if x20 f(x; 0) = elsewhere What is the maximum likelihood estimator of 0 ?
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- Let X(1),.., X(n) be the order statistics from Unif(0, 0). Obtain the joint distribution of (, X(m)) and show that they are independent. What is the distribution of ? X(m)Let the random variable X have the density function is given by F(e) =*. Os s5, lo, elsewhere. 1) The value of the constant C=; 2) The expected value of X is E(X)=; 3) The expected value of X2 is E (x2) =; 4) The variance of X is given by Var (X) =o? =.Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?
- Let Y1, Y2,...,Yn be independent random variables with Y; Poisson(A;). Show that the sum of these random variables S has a Poisson distribution with rate paramcter A = di.all pls dey are connected.What is the expected value of a continuous random variable X with probability density function (pdf) given by f(x) = 2x, 0 < x < 1?
- 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 you have a random sample of observations from random variables Xi, i=1, 2, .., n. Assume that X;'s are identically distributed and they have the following distribution function: f(x;;0) =o* (1–ơ), x; = 1,2 , 3., 0and variance of X if the probability mass function is f(x) = ; ;)" , Find the moment generating function, mean x = 1, 2, 3, 4, ...Let X1, X2,...X, be a random sample from f(x,e) = -.0 < x< 8, then T= max(X,} is a %3D complete statistic for the parameter 0 Select one: O True FalseSuppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?Find 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) 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