4. Let X and Y be independent, continuous random variables with densitiesandfx(x) ==fy (y) ==0{}if 0 < x < 2otherwise.y if 0

X and Y are independent Result: When X and Y are independent then f(x,y)=f(x)f(y)

Answered: 4. Let X and Y be independent,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

9 Let the probability density of the two-dimensional random variable (ξ, η) be (4e**, x > 0; f;(x)=• (0, 6e", y>0; -6y f,(v) =; 0, x<0. y<0. Find E(2 { +3 n ).
7. Let X and Y denote two continuous random variables. Let f(x,y) denote the joint probability density function and fx(x) and fy (y) the marginal probability density functions for X and Y, respectively. Finally let Z = aX + bY, where a and b are non-zero real numbers. (e) Derive an expression for Cov(Z) as a function of Var (X), Var(Y) and Cov(X,Y). [You may use standard results relating to variance and covariance without proof, but these should be clearly stated.]
Suppose (X, Y) is a joint continuous random variable with joint density function, f(x, y) = {cxy, for 1Y other words find the
Let x and y have joint density function * + 2y), for 0 3 Enter the exact answer. (1>}) - 3 1 (b) Find the probability thatx < + y. Enter the exact answer. px +
Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 0
(d) Let X, Y be independent Poisson random variables with X~ Poisson(1.5), Y~ Poisson (0.5). Compute the probability P(X + Y ≤ 2). Express your answer up to 3rd decimal place. (You shall use calculator to complete this problem.) Suppose two random variables X, Y admits density f(x, y) = 9 -x-3y 7(2x+y)e¯ " x, y ≥ 0, and f(x, y) = 0 for other (x, y). Compute the covariance of X, Y. Use the result to decide which of the following holds: Var[X + Y] .
Find the density of U = Y1 +Y2, where Y1 and Y2 are independent random variables with densities (yı – 1), 3 < Yı < 4, (y2 + 2), 0 < Y2 < 1, fy, (y1) : fy,(y2) = otherwise, otherwise.
4) The joint density function of the random variables X and Y is given by (&xy f(x, y) = 0SXS1,0 sysx otherwise Find (a) the marginal density of X, (b) the marginal density of Y, (c) the conditional density of X, (d) the conditional density of Y.
1. The joint density for the random variables (X, Y) is given below. for 0SS1,0SySI 0. for clsewhere (a) Find the marginal density of X (b) Find the marginal density of Y (c) Find VarlX] (d) Find VarV] (e) Are X and Y statistically independent? () Find P(X>0.6) (R) I EXY-0.8, find the correlation between X and Y
6. Let X and Y be continuous random variables with joint density function 24xy if 0 < x < 1,0 < y < 1 – x f (x, y) = 0. otherwise. Calculate E(Y|X = }).
4. Let X, Y be jointly continuous with density f(x, y) = = c(x - y)e-2 File Preview (a) Find the value of c. (b) Find the conditional distribution of X|Y. 0 < x<∞, -x < y < x otherwise

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

4. Let X and Y be independent, continuous random variables with densities {}} and fx(x) = fy (y) = = {}² if 0 < x < 2 otherwise. y if 0 < y < 2 otherwise. (a) Compute the density of X+Y. (b) Let Z = ¹ (X+Y) (that is, the Z is the average of X and Y). What is the density of Z?