Find the marginal density h(y) for the joint density function. Find the conditional density f(y/x). Find the conditional density f(x/y).
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- The 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) 0Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R, by 3. fx,y(x, y) = { Ay exp(-y(x+ A)), if a 2 0 and y > 0 0, otherwise. (i) Calculate the marginal density of Y. (ii) Let y > 0. Find the the conditional probability density function of X given Y = y. Interpret your answer. (iii) Calculate E[X|Y] and prove that E[X] = +oo. Hint: You can use without a proof that -dy = +oo. %3DVerify the claim that p (r) = p (x, y) dy, where p(r, y) and p (r) denote %3D the joint density and marginal density, respectively.The joint probability density function for X and Y is f(x, y). Find P(X < 0.7| Y = 0.5). Remember, you need to find the conditional density for X at Y = 0.5, then do the appropriate integration. f(x, y) = { i (2x + y) 0 < x < 1, 0Suppose X and Y have joint density f(x,y)=10x2y, 0<y<x<1. Find the marginal density of X.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.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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