1 f(x,y)=y The random variables X and Y have joint density function re", x>0, y>0 0, otherwise (1) Compute the marginal density function of Y, (2) Compute P(X>1|Y=y), (3) E[XY =y].
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f(x, y) = y
The random variables X and Y have joint density function
re", x>0, y>0
0,
otherwise
(1) Compute the marginal density function of Y,
(2) Compute P(X>1|Y=y),
(3) E[XY =y].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb862d3b-6924-4e7d-9718-fbd9f38b9b4c%2F2523ebd3-b0ad-45b0-b9da-463d9ce9ceaf%2Fecy96a8_processed.png&w=3840&q=75)
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- The joint probability density function of two dimensional random variable(X,Y) is given 8 by f(x, y) = xy, 13xsys2 9 = 0, elsewhere Find the marginal density functions of X and Y.The density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),Let X and Y be continuous random variables having a joint pdf given by f(x, y) = e-*, 0sysx 3).
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- • Find the density of Z = (X+ Y)2, where X and Y are independent uniform random variables over (-1, +1).Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysxLet 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.Two non-negative random variables X and Y have a joint density function f(x, y) = re-*v +1) x > 0, y > 0 Find the correlation coefficient.3) The joint probability density function of the random variables X, Y, and Z is ², 0 }, 1SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
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