Homework Help is Here – Start Your Trial Now!
Math
Probability
Let the joint density function of X and Y be given by e-(y+#) for 0 < x, y < ∞», fx,y (x, y) otherwise. (a) y ncing the marginal denoity 9), Show that (b) (i) For y > 0, determine fx|Y (x\y), the conditional density of X given that Y = y. Explain (without calculation) why, for y > 0, E[X|Y = y] = y. Hence, or otherwise, show that E[X] = 1. %3D

Let the joint density function of X and Y be given by e-(y+#) for 0 < x, y < ∞», fx,y (x, y) otherwise. (a) y ncing the marginal denoity 9), Show that (b) (i) For y > 0, determine fx|Y (x\y), the conditional density of X given that Y = y. Explain (without calculation) why, for y > 0, E[X|Y = y] = y. Hence, or otherwise, show that E[X] = 1. %3D

A First Course in Probability (10th Edition)
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
icon
Related questions
Question

Probability. Only question bi. 

Let the joint density function of X and Y be given by (le-(y+÷) for 0 < x, y < ∞, fx.x(r, y) : otherwise. (a) Sy nding the marginal denoity 9), Show that (b) (i) For y > 0, determine fxy(x\y), the conditional density of X given that Y = y. Explain (without calculation) why, for y > 0, E[X|Y = y] = y. Hence, or otherwise, show that E[X] = 1.
Transcribed Image Text:Let the joint density function of X and Y be given by (le-(y+÷) for 0 < x, y < ∞, fx.x(r, y) : otherwise. (a) Sy nding the marginal denoity 9), Show that (b) (i) For y > 0, determine fxy(x\y), the conditional density of X given that Y = y. Explain (without calculation) why, for y > 0, E[X|Y = y] = y. Hence, or otherwise, show that E[X] = 1.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer