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- [Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0Let random sample of n observations from each of the distributions: a. Poisson distribution with parameter θ. b. f(x, θ) = (1/ θ) e-x/θ , 0 < x. In each case find the Minimum Variance Estimator of θ and prove its efficiency.Given (x + 2y) ,01. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwise1. Let X be a random variable with pdf f(x) = 1,0 3).The random variable X takes value O with probability, and value 1 with the remaining probability. The random variable Y takes value 100 with probability and value 101 with the remaining probability. What is the relation between the variance of X and the variance of Y? Var[X] Var[Y] "Given pdf f (x) = 1.5x2 for −1< x < 1. Determine variance of X.f(X)= 3/8( 4x - 2x2 ) 0<* x <* 2 (* less or equal to) a. Find the variance of X.Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows. 2 3 4 P(x) 0.1 0.2 0.1 0.2 0.4 Send data to Excel1. 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.SEE 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