What is the Expected Value of (X/Y)?

Click For Summary

Homework Help Overview

The problem involves calculating the expected value of the ratio of two discrete random variables, X and Y, given their joint probability density function. The context centers around understanding the properties of expected values in relation to discrete probability distributions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of calculating E[X/Y] and question the appropriateness of using integrals for discrete random variables. Some suggest evaluating the expected value by considering each state of the random variables directly.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the nature of the probability function and the implications for the calculation method, but no consensus has been reached.

Contextual Notes

There is a noted confusion regarding the use of integrals in the context of discrete random variables, as well as the proper application of expected value properties. Participants are questioning the assumptions made in the original poster's approach.

Samwise_geegee
Messages
6
Reaction score
0

Homework Statement


Let x and y be discrete random variables with joint probability density function

P(X,Y)= 2X-Y+1/9 for x=1,2 and y=1,2
0 Otherwise

Calculate E[X/Y]


Homework Equations



E[XY]= ∫∫XYP(X,Y)dxdy



The Attempt at a Solution



I can't find a property of Expected value to make E[X/Y] solvable. This is my best guess.
E[X/Y]= ∫∫X*1/YP(X,1/Y)dxdy

E[X/Y]=∫∫X*1/Y*(2X-1/Y+1/9)dxdy from 1 to 2 on the first integral and 1 to 2 on the second integral
 
Physics news on Phys.org
looks like you have a discrete probability function there.
there are only 4 states, so why not work out X/Y for each state and find the expectation by weighted sum?
 
I'm just not sure how to calculate E(X/Y). Is what I wrote right?
 
You can answer that one yourself!

Consider: what you wrote involves some integrals.
Are integrals associated with continuous or discrete probability functions?
What kind do you have?
 
Samwise_geegee said:
I'm just not sure how to calculate E(X/Y). Is what I wrote right?

What you wrote is wrong. You seem to be suffering from the disease of writing formulas without knowing what they mean or when they should be used, and the prognosis of that disease is not good. Integrals are used with continuous random variables having probability density functions. Do you see any such random variables in your problem?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
11
Views
3K
Replies
29
Views
5K
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K