Determine the value of e that makes the function f (x, y) = c(x + y) a joint probability density function over the range 0 < x < 3 and 0 < y < 3
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- Let X be a random variable of a continuous type and let it be given by Mx(t) = 1 t<1 (1-t)² Find the probability density function of X.The composite probability density function of continuous random variables X and Y is given as f (x, y) = c (x²+y²) , 0 <x <1, 0 <y <1. (a) Calculate the constant c.(b) Calculate the marginal probability functions of the continuous random variables X and Y.(c) Calculate the probability P (0<X<1/2 , 1/2<Y<1).The probability density function is f(x) = c(1-x^2 ) -1<x<1 Find interquartile range.
- Let X be a random variable with probability density function [ a + bx², 0X is a random variable whose cumulative distribution function F(x) satisfies F(1) = 13, F(2) = 34, and F(3) = 1 • Make X discrete and give its probability mass function.• Make X continuous and give its probability density function.Let f(x) = Ce-x/1+e-2x for all x in (-infinity, infinity). If f is a probability density function for a random variable X on (-infinity, infinity), answer the following: (a) Find the value of constant C. (b) Evaluate the probability P(X<-4). Correct to four decimal places.Recommended 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