6) g and h 6)- Let x and y have the joint densityf(x, y) ={x +cyif 1

Name: 6) g and h 6)- Let x and y have the joint densityf(x, y) ={x +cyif 1
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Description: 6) g and h 6)- Let x and y have the joint densityf(x, y) ={x +cyif 1

The joint probability density function is: f(x,y) = x+cy for 1≤x≤2 ; 0≤y≤1 = 0 otherwise The…

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6) g and h

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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

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Question

6) g and h

6)- Let x and y have the joint density
f(x, y) =
{x +cy
if 1<x< 2; 0 <y<1
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
| fy(y)dy = 1
-00
c) Find f,(x\y), 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.

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