uppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the co

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
Question

Suppose the random variables X and Y are inde lent and identically distributed. Let Z =aX +Y. If the correlation coefficient between X and Z is1/3 , then what is the value of the constant a ?

Exercises
1. Suppose that X1 and X2 are random variables with zero mean and unit
variance. If the correlation coefficient of X1 and X2 is –0.5, then what is the
variance of Y = =k2Xk ?
Lk=1
2. If the joint density of the random variables X and Y is
if (x, y) E { (x,0), (0, -y)|x, y = -2, –1, 1,2}
f(x, y)
otherwise,
3. Su
the random variables X and Y are inde
lent and identically
distributed. Let Z = aX +Y. If the correlation coefficient between X and
Z is , then what is the value of the constant a ?
Transcribed Image Text:Exercises 1. Suppose that X1 and X2 are random variables with zero mean and unit variance. If the correlation coefficient of X1 and X2 is –0.5, then what is the variance of Y = =k2Xk ? Lk=1 2. If the joint density of the random variables X and Y is if (x, y) E { (x,0), (0, -y)|x, y = -2, –1, 1,2} f(x, y) otherwise, 3. Su the random variables X and Y are inde lent and identically distributed. Let Z = aX +Y. If the correlation coefficient between X and Z is , then what is the value of the constant a ?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Continuous Probability Distribution
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