2.6 Solve the below problem: Let Y, and Y2 have joint density function Se-Os+y2), f(y1»Y2) = {{o, Yı 2 0, y2 2 0, elsewhere. 0, 2.6.1 Find the marginal density function for Y,. Identify this density. 2.6.2 For any y2 > 0, what is the conditional density function of Y given that Y2 = y2? %3D
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- 7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.6. The joint probability density function of X and Y is given by 6 f(z,v) = (- ÷(² +).0 Y). (c) Find P(Y > |X < }). (d) Find E[X].Find Mass, Mx, My and I and of the Lamina bounded by R = {(x, y) | 0 ≤ x ≤ 2, -5 ≤ y ≤ 5} and with the density function p(x, y) = 4-z-y². Provide an answer accurate at least 4 significant digits. Lamina Problem 04 05 08 Lamina (green) and Density Function p(x,y) Note: The graph is an example. The scale and equation parameters may not be the same for your particular problem. Mass= Mx = My I= ÿ = Hint: Suggest using the rectangular coordinate system.
- 62For x, y ≤ (0, ∞), let X and Y have the joint density 1 -e Y f(x, y) = Y i) Compute the marginal density of Y. ii) Compute the conditional mean and variance of X given Y = y. iii) Compute Var(X).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. %3D
- Let X, Y have the joint density function 2 \exp(-x-y) if Are they independent? Find Cov(X,Y). 0Calculate cov(X,Y)1.) Suppose X and Y have joint density function f(x,y)= 8xy/3 on x is greater than or equal to 0 and less than or equal to 1. and y is greater than x and is less than or equal to 2x. a.) Find P( Y< 0.8) b.) Find the marginal density function of X c.) What is E(X)?5) For the following density function f(x) = c x2 (1–x), 0Now, assume that Y₁,..., Yn distributed iid, each with density -{* where is positive constant. Find the density function for fy) (y). fy(y) = e-(-0), 0, if y> 0; otherwise,2. Consider the joint density function 16M f(x,y) = {#, z> 2,0SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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