Homework Help is Here – Start Your Trial Now!
Math
Statistics
p. Let Z Let X, Y be independent geometrically distributed random variables with parameter = E[X|X + Y]. Find the expected value and the variance of Z. Hint: E[X + Y|X+Y] = X + Y. =

p. Let Z Let X, Y be independent geometrically distributed random variables with parameter = E[X|X + Y]. Find the expected value and the variance of Z. Hint: E[X + Y|X+Y] = X + Y. =

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

Pvg

Let \( X, Y \) be independent geometrically distributed random variables with parameter \( p \). Let \( Z = \mathbb{E}[X \mid X + Y] \). Find the expected value and the variance of \( Z \). Hint: \(\mathbb{E}[X + Y \mid X + Y] = X + Y\).
Transcribed Image Text:Let \( X, Y \) be independent geometrically distributed random variables with parameter \( p \). Let \( Z = \mathbb{E}[X \mid X + Y] \). Find the expected value and the variance of \( Z \). Hint: \(\mathbb{E}[X + Y \mid X + Y] = X + Y\).
Expert Solution
Step 1: Determine the given variable

Given:
X, Y are independent geometrically distributed random variables with parameter p.
The expected value and variance for a geometrically distributed random variable are:

E left parenthesis X right parenthesis equals 1 over p Var left parenthesis X right parenthesis equals fraction numerator 1 minus p over denominator p squared end fraction

Likewise, for Y:

E left parenthesis Y right parenthesis equals 1 over p Var left parenthesis Y right parenthesis equals fraction numerator 1 minus p over denominator p squared end fraction

steps

Step by step

Solved in 3 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar 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
SEE MORE TEXTBOOKS