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- Suppose X = 1/(1+Y), where 3 Y ~ fy(y) = 12 1+y y > 0, 0, otherwise. Identify the distribution of X by name and parameter values.O FIND THE EQUATIONS OF THE TANGENT NORMAL LINES TO THE 0 o 2 - 6x +2y: 2 AURVE : Xty"-6x + 2y -O © (0,0) %3DLet X1, X2, ..., Xn be a random sample from the distribution with the pdf f(x; theta) = theta*x^(theta-1), 0<x<1, 0<theta<infinity, zero elsewhere. Find the mle theta-cap of Theta.
- Find kurtosis by using ungroup data given in the picture using quartile deviation, make sure to arrange data before solving question.2) Let X be a continuous random variable with PDF 0vaim of the function find the average fcx) = x² = 5x + 6 cosx on th Interval [-1,³].Show the derivation of the formulas Mean and Variance of Normal Distrubution (commonly used parametric families of continuous densities).Suppose X - Fm,n- a) Find the distribution of 1/X. b) Find the distribution of (m/n)X Y = 1+ (m/n)X' Identify the distribution with appropriate parameters.Let X1,...Xn be iid Normal(θ + c, σ^2), where c and σ^2 are known constants (i.e., E(Xi) = θ + c). Find a sufficient statistic for θ. Use this sufficient statistic to obtain an MVUE for θ.5. Let (*1, x2, ., Tn) be a random sample from the distribution f (x) = Ax^-1; 0 0. Find the moment estimator of A.he average American gets a haircut every 41 days. Is the average larger for college students? The data below shows the results of a survey of 16 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 38, 40, 44, 39, 50, 53, 47, 46, 51, 40, 49, 42, 38, 43, 54, 45 What can be concluded at the the αα = 0.05 level of significance level of significance? The test statistic Correct = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 3 decimal places.) The p-value is αα Based on this, we should the null hypothesis.Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{OSEE 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