Given f(x,y) = [x*sqrt(y)] / 3224 , 0<x<y<5.76 (f(x,y)= 0 otherwise)
Find P(x + y > 0.5 | x = 1/5)
Given f(x,y) = [x*sqrt(y)] / 3224 , 0<x<y<5.76 (f(x,y)= 0 otherwise) Find P(x + y >...
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50) 0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
0, otherwise Let f(x,y)= 3. Sketch the region of integration Find k. Find P(X |Y 1/4) Find P(X |Y=1/4) a. b. c. d.
6. Let f(x,y) = 1 if 0 < y < 2x, 0<x<1, and 0 otherwise. Find the following: a) f(y|x) b) E(Y|X = x) c) The correlation coefficient, p, between X and Y
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find 2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
The density f(x,y) is given by the formula f(x,y) = 8x(x + y), x ≥ 0, y ≥ 0, x + y ≤ 1 and zero otherwise. (a) Find the marginal distributions. (b) Find the conditional distribution of Y given X = x. (c) Find P(X ≤ 1/2, Y ≤ 1/2) (d) Find P(X ≤ 1/2) (e) Find P(Y ≤ 1/2 | X ≤ 1/2) (f) Find P(Y ≤ 1/2 | X = 1/2)
The Joint pdf of X and Y is f(x,y) = for 0<x<y<1, and 0 otherwise. a) Find b) Find ا اتت (1+ Ty2 P(X E(X Y = y)
For all of the following, consider the joint pdf f(, y) c(3ry) for a, yE (0, 1 and 0 otherwise. 5. Given a random sample of 100 observations from X, find P(.5 < X HINT: Use the CLT .55) For all of the following, consider the joint pdf f(, y) c(3ry) for a, yE (0, 1 and 0 otherwise. 5. Given a random sample of 100 observations from X, find P(.5
13. The random variables X,Y are jointly continuous with the jpdf 0 otherwise (a) Find P(2Y>X). (b) Find the conditional expectation E(XY -0.5).
Consider the random variables X and Y with joint density function [5] f(x,y)=1/x , 0<y<x<1 i) Find P(X > 0 . 5 , y >0.5). ii) Find fX | y(x) and fY | x(y)..
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...