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Find a constant k (in terms of a) so that the function fxx (x,y) = e-(x+u)...
4.3-8 (a) Find a constant b (in terms of a) so that the functionomit o ovi tbe be x+y) 0<x<a and Assum Problem 0<y< fx.y(x, y)= Work Proble elsewhere is a valid joint density function. nt ob lanigu (b) Find an expression for the joint distribution function. d oninst () 4.2-10. Discrete random variables X and Y have a joint distribution function Fx.y(x,y) 0.10u(x+4)u(y-1)+0.15u(x +3)u(y+5) +0.17u(x+1)u(y-3) +0.05u(x)u(y-1) +0.18u(x-2)u(y + 2) + 0.23u(x-3)u(y-4) +0.12u(x-4)u(y +3) Dete
4. Let X and Y have joint density function le-x 0 < y < x < 0 Jxy(x, y) = lo elsewhere Another random variable of interest is U=X–Y. Find the probability density function for U.
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))
4. Let X and Y have joint probability density function ke 12-00o, 0< y< oo 0, otherwise where k is a constant. Calculate Cov(X, Y).
2. Suppose X and Y have the joint pdf fxy(x, y) = e-(x+y), 0 < x < 00, 0 < y < 0o, zero elsewhere. (a) Find the pdf of Z = X+Y. (b) Find the moment generating function of Z.
< 1. The joint probability density function (pdf) of X and Y is given by for(x, y) = 4 (1 - x)e”, 0 < x <1, 0 < (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY).
answer should be 2x 5. Let X andY joint density function if 0r< 1; 0 <y<r 8.ry f(r,y) = 0 elsewhere. What is the regression curve y on r, that is, E (Y/X = r)?