] The joint density function of two continuous random variables X and Y is: Scx²e-y/3 1
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- L_E_T Y and X be t_w_o discrete random variables whose joint p_r_o_bability function is given as shown in the table. Find the marginal distribution f x(x) of random variable X. Find the cumulative distribution function Fy(y) of random variable Y.Two random variables X and Y with a joint PDF f(x,y) = Bx+y for 0≤ x ≤6 , 0≤ x ≤7 and constant B Find value of constant B7. Let X and Y be continuous random variables with joint probability density function given by fxy(xy): Sc, (0, 0 < x < y < 1 otherwise a) Find the value of c. b) Find the marginal distributions of X and Y. c) Find the conditional distribution of Y given X. d) Find the E(Y) and Var(Y).
- The probability density function of a variate X is as follows, 1 2 3 4 P(X) k 3k 5k 7k 9k 11k 13k Find the value of, (i) k (ii) P(X < 4) (iii) P(3 < X < 6).The total number of hours, measured in units of 100 hours, that a family uses a vacuum cleaner in a period of one year is a continuous random variable X that has the following density function:X que tiene la siguiente función de densidad: 0Let X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.(b) Determine the marginal distributions of X and then of Y. (c) Find the conditional distribution of Y|X = x.The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8The discrete random variables X and Y have the following joint probability function Y 0 1 2 1 1/20 2/20 3/20 X 2 2/20 1/20 4/20 3 3/20 1/20 3/20Recommended 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