6)- Let x and y have the joint density f (x, y) = {* + cy if 1< x< 2; 0 < ys1 %3D elsewhere where c is a constant a) Find the value of c that makes f(x, y) a probability density function. b) Find the marginal density for y and show that frV)dy = 1 c) Find f1(xly), the conditional density for x given y.

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...
icon
Related questions
icon
Concept explainers
Topic Video
Question
6) a, b, and c
6)- Let x and y have the joint density
f(x, y) = {* + cy if 15x< 2;0<ys1
elsewhere
where c is a constant
a) Find the value of c that makes f(x, y) a probability density function.
b) Find the marginal density for y and show that
O)dy = 1
c) Find f1(xly), the conditional density for x given y.
d) Find E(x)
e) Find E(y)
f) Find E(x + y)
g) Are x and y independent?
h) Find the covariance of the random variables x and y.
Transcribed Image Text:6)- Let x and y have the joint density f(x, y) = {* + cy if 15x< 2;0<ys1 elsewhere where c is a constant a) Find the value of c that makes f(x, y) a probability density function. b) Find the marginal density for y and show that O)dy = 1 c) Find f1(xly), the conditional density for x given y. d) Find E(x) e) Find E(y) f) Find E(x + y) g) Are x and y independent? h) Find the covariance of the random variables x and y.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON