Let X be a random variable whose density is given by the formula f(x) =  cx2  if    x ∈ (0, 2)           0     if   otherwise. (a) Find c. (b) Let Y be the integer part of X, i.e., Y = 0 if 0 ≤ X < 1 and Y = 1 if 1 ≤ X < 2. Let Z be the fractional part of X, i.e., Z = X −Y . Find the correlation between Y and Z.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Let X be a random variable whose density is given by the formula
f(x) =  cx2  if    x ∈ (0, 2)
          0     if   otherwise.
(a) Find c.
(b) Let Y be the integer part of X, i.e., Y = 0 if 0 ≤ X < 1 and Y = 1 if 1 ≤ X < 2. Let Z be the fractional part of X, i.e., Z = X −Y . Find the correlation between Y and Z.

Expert Solution
steps

Step by step

Solved in 2 steps with 7 images

Blurred answer
Knowledge Booster
Multivariate Distributions and Functions of Random Variables
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman