Given the joint density function: (6 – x – y f(x,y) = if 0 < x < 2 and 2 < y < 4; 8 otherwise. The marginal distribution h(y) is:
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- 10. Suppose X and Y have a joint density function given by Sca?, for 0< x < y < 1, 10, f(x, y) otherwise. Find c, the marginal density functions, EX, EY, and the conditional expectations E(Y | X = x) and E(X | Y = y).Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density f(x, y) = = { x ² + 30.10. +,01) Prove that the density for the standard normal distribution Satisfies: f(x) = 1 √2π ∞ 1₁ -8 f(x) dx = 1b) Let X and Y be jointly continuous random variables with the following joint density function (1/32)xy ,0 2) v. Evaluate P(Y > X – 2)Let 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. %3DCont?Let X, Y have the joint pdf for x? + y? 0, y > 0 fx,y O.w. where c is some constant. Question part 4: find fy (y), the marginal distribution of Y. (Answer choices are given in terms of c) O fy (y) = ;(1 – y²) for 0Let Y, and Y, have joint density function y1 2 0, y2 2 0, elsewhere. e-Ox+yz), What is P(Y, + Y2 < 3)? Assume that the marginal distributions for Y, and Y, are exactly the same and that Y, and Y, are independent. What is the E(Y, + Y,)?Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON