Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.
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Let random variables X and Y have the joint
fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1
0, otherwise
Find the joint pdf of U = X^2 and V = XY.
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- What is the cdf of the given pdf functionSuppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) = 2β. Further, suppose that given X = x , the RV Y has the Unif (0, x) distribution. a) Write down the conditional pdf of Y given X = x (f_Y|X )(y | x) = b) Find the joint pdf of (X,Y) (f_XY)(x,y)= c) Find the conditional mean and variance of Y E(Y | X=x) =____________ V(Y |X=x )= ____________ d) Find the unconditional mean and variance of Y E( Y)= ____________ V(Y ) =____________ e) Find the marginal pdf of Y (f_y)( y)= ___________ f) Identify the distribution of Y Y-_________ g) Use parts e)- f) to find mean and variance of Y E(Y )=____________ V( Y)= ___________ The answer for Is 1/x (0<y<x) Β2 x/2 , (x2)/2 β , β please solve e) and f) and g)fx'.In xdx = ?
- a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results. Calculate E[X2]. (b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.2. Let X and Y be jointly continuous random variables with joint PDF x + cy2 0, OSXS1,0Sys1 elsewhere a) Find the constant c Find the marginal PDF's fy(x) and fy(y) c) Find P(OSXS1/2,0SYS1/2) b)Let X be a continuous random variable with a pdf given by f(x) = (3x^2)/2 where x lies in the closed interval [-1,1]. Evaluate P(x>1/2). Select the correct response: 7/16 8/17 2/17 7/8
- Let X and Y be two continuous random variables with joint probability density [3x function given by: f(x,y)= 0We have a random variable X and Y that jave the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} Let U = Y - X2. What is the support for the random variable U? Are there critical points? If U = Y/X. What is the support for the random variable U? Are there critical points?(b) Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by f(x)=K(6-x), 0SEE 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