Suppose that the joint distribution function of X and Y is given by f (x, y) =x+y If 0 < x < 1 and 0
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![Suppose that the joint distribution function of X and Y is given by
f (x, y) =x+y
If 0 < x < 1 and 0 <y<1, and 0 otherwise, find:
a. the marginal density of X
b. the marginal density of Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31b7b43f-c29e-4d4f-9b0f-fb4cc8b29bc5%2Fd5f378b1-2c39-470f-baf9-98e8424ba866%2Fto6i4tx_processed.png&w=3840&q=75)
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- Let X and Y be two random variables with joint density function 2, 0 < x < y < 1, fx,y (x, y) 0, O.W. Find the marginal density function of the random variable X and find the marginal density function of the random variable Y7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0Find the cumulative distribution function for Y if its density is f(y) = { 2(1 – 1/y²), 1 1.5).If the joint density function of X and Y is given f(x, y) = {k(x + 2y), 0 < x < 1; 1 < y< 2 0, elsewhere <(x - a. Evaluate the value k. b. Estimate P(X+Y < 2). C. Find the marginal distribution of X and the marginal distribution of Y.Continuous variable X is distributed on the interval [b,c] = [24.4, 64.6] according to the density curve shown below. As indicated by the plot, the distribution of X is symmetric. What is the mean of this distribution equal to? If there is not enough information to answer this question, enter 0 below. Otherwise, enter the value of the mean. f(x) b сThe joint probability function of random variables X and Y is given to be: 3x - y 1The joint probability density of X and Y is f(x, y). Find the marginal density of X at 0.4. The answer should be given to 2 decimal places. g(0.4) = f(x, y)= { 2(x + y) 0The graph shows the uniform density function for a friend who is x minutes late. Find the probability that the friend is at least 15 minutes late."Medians, etc problem." Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.The joint probability function of random variables X and Y is given to be: 3x- y 15x<41he length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.Y1 2. Suppose that Y,~ exp(1) and Y2~ exp(1). Let U = Y1+Y2 and V = Y1 + Y2. a. Determine the joint density of U and V. b. Find the marginal distribution of U. c. Find the marginal distribution of V. d. Establish whether U and V are independent.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