Suppose X and Y has the joint density
f(x, y) = 6xy(2 – x – y), 0 < x <1 , 0 < y < 1,then find E(X /Y = y).
ANSWER:
4. Suppose X and Y has joint density f(x, y) = 2 for () < x <y<1. (a) Find P(Y - X > 2). (b) Find the marginal densities of X and Y. (c) Find E(X), E(Y), Var(X), Var(Y), Cov(X,Y)
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)
2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1 <r< 1 and -1 <y<1, and 0 otherwise. Here is a constant. (a) Determine the value of C. (b) Are X and Y independent? (Explain why or why not.) (c) Calculate the probability that 2X - Y > 0 (d) Calculate the probability that |X+Y| < 2 3. Suppose that X1 and X2 are independent and each is standard uniform on (0,1]. Let Y...
2. Suppose X and Y are continuous random variables with joint density function f(x, y) = 1x2 ye-xy for 1 < x < 2 and 0 < y < oo otherwise a. Calculate the (marginal) densities of X and Y. b. Calculate E[X] and E[Y]. c. Calculate Cov(X,Y).
Problem #8: Suppose that X and Y have the following joint probability density function. f(x,y)- ^x, 0 < x < 5, y> 0, x-2 <y <x+:2 146 (a) Find E(XY (b) Find the covariance between X and Y.
Problem #8: Suppose that X and Y have the following joint probability density function. f(x,y)- ^x, 0
1. Suppose the joint density of X and Y is given by f(x,y) = 6e-3x-2y, if 0 < x < inf., 0 < y < inf, 0 elsewhere. Part A, Find P( X < 2Y) Part B, Find Cov(X,Y) Part C, Suppose X and Y have joint density given by f(x,y) = 24xy, when 0<= x <=1, 0 <= y <=1, 0 <= x+y <=1, and 0 elsewhere. Are X and Y independent or dependent random variables? why?
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
Q2. . Suppose X and Y have joint density hr'y, x20,y 20, z y< 1 f(x, y) 0, otherwise Find h to make f(z, y) a legitimate density function. Then find the marginal distribution of X
(4) Suppose that the joint density function of X, Y and Z is given by )<y <<< 1 f(x, y, z) = { otherwise. (a) Find the marginal density fz(z) (b) Find the marginalized density fxy(x, y) 72 (c) Find E (2)
4. Suppose two random variables X and Y has the following joint density function Cry, 22 Sy<1, f(x,y) = { 0, otherwise. (a) Find the constant C. (b) Find E(Y|X = 1/2). 5. Suppose X1, X2, ..., are i.i.d. random variables coming from the N(0,0%) population. (a) Determine the mean and variance for X. (b) Show that va bos (x2) – 1o60*) $ (0.2).