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- Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure of the right and left tires are random variables X and Y respectively, with the joint p.d.f. f(x, y) = K(x^2+ y^2) when 20 < X < 30 and 20 < y < 30 and zero otherwise. Determine the marginal distribution of air pressure in the right tire alone. (Leave it in terms of K)don't copy from cheggWhat are the expected value and the standard deviation of the area of the circle whose radius is a random variable X with density function f(x) = 1 for 0 < x < 1 and f(x) = 0 otherwise ?
- The joint distribution of X and Y is: Pxy(0,0)=1/25, Pxy(0,1)=a, Pxy(0,2)=2/25 Рxy(1,0)-а, Рx(1,1)-b, Рҳ/(1,2)-а Рxy(2,0)-2/25, Рxx(2,1)-а, Рҳ/(2,2)-1/25 You want "a" to make the variance of Y as minimum as possible. X,Y X,Y 1. Fir The variance of Y equals. Tin Select one: а. 1/2 b. 6/25 с. 2/5 d. 3/5 e. 3/10Suppose 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., 0Let 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 FalseTwo random variables X and Y have joint char- acteristic function l@,,m)=exp(-20,?-80;) (i) Show that X and Y are zero mean ran- dom variables.Let X and Y be two random variables with joint probability mass function: p(x,y) = xy(1+y) for X=1,2,3 and Y=1,2 p(x,y) = 0, Otherwise. Please enter the answer to 2 decimal places. • What is the variance of (4-5X)?4. The probability density function of a continuous random variable } is: (1 + x) f(x) = if -1 < x < 0 3 (3 - 2x) if 0 ≤ x < ₂ < ²³/ 15 Derive the distribution function of ! (Solution: 0, if x≤e1 if-1The joint continuous distribution of random variables X and Y is given by f X,Y(x,y) = l2exp[-lx] for 0 < y < x < ∞ for some parameter l >0. = l2exp[-lx] * I[ 0 < y < x < ∞ ] Are X and Y independent? Explain. Identify the marginal distributions of X and Y by type and parameter values. (No conditioning-just state type of distribution)If X|0 ~ Bin(n, 8) and 0 - Beta(a, B), show that the posterior distribution of 0 given X is a beta distribution with parameters x + a and n-x +B. Note: f(x\0) = () 0*(1– 0)"-* Г(а + В) h(0) Г(а)Г() ea-1(1 – 0)B-1 andRecommended 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