6. The random variable X is distributed by f(z)=e, z>0. What is the density, g(y), of where it is non-zero? A. 1 X²¹ V 2y³/2 B. 2√3 C. 29-√7 D). -1/47 -1/ E. e
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![6.
The random variable X is distributed by f(z)=e, z>0. What is the density, g(y), of
where it is non-zero?
A.
1
X²¹
2y³/2
B.
2√9
C.
29-√7
D).
-1/47
-1/
E. e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46ef9537-1ee2-4049-8de2-a5a2651d41f3%2Fe0106983-f9db-4486-9682-e1ea46930721%2F4y47mrd_processed.jpeg&w=3840&q=75)
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- 1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.The random variables X and Y have ä joint Probability masS 6 function as Follows - (X.Y); For ( X,Y) E A 18 For the other (x,Y) while A = {(x,Y ,2,3 end y=l,2} ore Depine: %3D a The probability mass Function For the random variable V= X+ Y b) The probability mass Function For the random variable V= X-Y 285The random variable Y is defined by Y = - (X + \X1), where X is another RV. %3D Determine the density and distribution function of Y in terms of those of X. 44
- Q 4.2. Let (X, Y) be a random variable with the following density: 15x²y 0 0 < x < y < 1, otherwise. fx,y(x, y) = { { 1. Express E(YX) in terms of X. 2. Express Var(X|Y) in terms of Y.Q27. Statiçally independent random variables X and Y have respective densities, f,(x) = 5u(x) exp(-5x) af,(y) = 2u(y) exp(-2y), find the density of the sum W = X+ Y.The PDF of a random variable Y is Sy/2 02. Let X and Y denote independent random variables with respective probability density func- tions fx(x) = 2x, 04. Find the average value of the sum of the squares of two numbers x and y where (b) x + y| < 1 and x - y| < 1.Consider a random variable Y with density S (1/2)(y + 1), -1 < y < 1, else. f(y) Calculate E(W) and V(W) for the random variable W = 4+Y – 2Y².Q 4.2. Let (X, Y) be a random variable with the following density: {152-2 0 £x,x (x, y) = { 1. Express E(Y|X) in terms of X. 2. Express Var(XY) in terms of Y. 0 < x < y < 1, otherwise.5. Let X be a random variable whose density is given by the formula cx? if x E (0, 2) f (x) = otherwise. (a) Find c. (b) Let Y be the integer part of X, i.e., Y = 0 if 0 < X < 1 and Y = 1 if 1tEx. 4. Let X,Y are independent random variables where X ~ N(0, 1) and Y ~ G(1/2, n/2). Let T:= X//Y/n, then show that the density function of T is described as r(n+1)/2) (1+) VnnI'(n/2) -(n+1)/2 fr(t) - (-∞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