The function below is a joint CDF of two continuous X, Y: iD else 1. Find the constant c and the ...
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
2. Let X and Y be two continuous random variables varying in accordance with the joint density function, fx.y(z, y-e(x + y) for 0 < z < y < 1. Solve the following problem s. (1) Find e, fx(a) and fy (v) (2) Find fx-u(z) and fY1Xux(y) (8) Find P(Y e (1/2, 1)|X -1/3) and P(Y e (1/2,2)| X 1/3). 3. Find P(X < 2Y) if fx.y(zw) = x + U for X and Y each defined over the unit...
a. Given the joint probability den- sity function fxy(x, y) as, Skxy, (x, y) e shaded area Jxy(, 9) = 10 otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? b. Given the joint probability density function fxy(x, y) as, fxy(x, y) = { 0 kxy, (x, y) E shaded area otherwise Find [i] k [ii] fx(x) [iii] fy(y) Are X and Y independent? 2 1
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
The joint density function of continuous variables X and Y is (8 points) fry (x, y) = x y ; 0 < x < 1, 1 < y < 5 and= 0 elsewhere. i. Find the marginal density functions for X and Y, fx (x), fy (y). ii. Are X and Y independent?. Justify your answer.
0〈z,0〈y Given the following joint distributionfrY(x,y)-, cez+2y else Calculate the following 1. The value of c that makesfxy a proper pdf 2. The marginal distribution function fx(z) 3. The marginal distribution function fy () 4. P(X 1) 7. The random variables X and Y are independent if it is possible to write fxy (x, y) as the product of Íx (x) and fy (y) such that/xy(z, y) = k . Íx (x) . fy(y) for some value of k. Are...
0 〈 y 〈 x2く1· Consider two rvs X and Y with joint pdf f(x,y) = k-y, (a) Sketch the region in two dimensions where fx,y) is positive. Then find the constant k and sketch ) in three imesions Then find the constant k and sketch f(r.y) in three dimensions (b) Find and sketch the marginal pdf fx), the conditional pdf(x1/2) and the conditional cdf FO11/2). Find P(X〈Y! Y〉 1/2), E(XİY=1/2) and E(XIY〉l/2). (c) What is the correlation between X...
0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 – x)y for 0 < x < 1, (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y. (d) Find Pſy < 81/2],P[X<Y]. (e) Are X and Y independent? (f) Find the correlation and covariance of X and Y. (g) Determine whether X and Y are uncorrelated. (h) Find fy(y|x) (i) Find E[Y|X = x]...
2. Suppose X and Y are independent continuous random variables. Show that P(Y < X) = | Fy(x) · fx (x) dx -oo where Fy is the CDF of Y and fx is the PDF of X [hint: P[Y E A] = S.P(Y E A|X = x) · fx(x) dx]. Rewrite the above equation as an expectation of a function of X, i.e. P(Y < X) = Ex[•]. Use the above relation to compute P[Y < X] if X~Exp (2)...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...