How do i calculate expectation of expectation?

  • Context: Graduate 
  • Thread starter Thread starter AndreTheGiant
  • Start date Start date
  • Tags Tags
    Expectation
Click For Summary
SUMMARY

The discussion focuses on calculating double expectations, specifically E(E(X)) and E(E(XY|X)). The key takeaway is that each expectation should be evaluated sequentially. For instance, if E(X) equals 4, then E(E(X)) also equals 4. The principles of expectations, such as the ability to factor out constants, are essential for simplifying these calculations.

PREREQUISITES
  • Understanding of basic probability theory
  • Familiarity with the concept of expectation in statistics
  • Knowledge of conditional expectations, specifically E(XY|X)
  • Basic understanding of random vectors and their properties
NEXT STEPS
  • Study the properties of expectation in probability theory
  • Learn about conditional expectations and their applications
  • Explore the concept of random vectors and their expectations
  • Review examples of double expectations in statistical contexts
USEFUL FOR

Students and professionals in statistics, data science, and mathematics who are looking to deepen their understanding of expectation calculations and their applications in probability theory.

AndreTheGiant
Messages
26
Reaction score
0
When i have stuff like

E(E(X)) or E(E(XY|X)) etc how do i evaluate a double expectation?

and for random vectors stuff like

E(E(X)'Y) or E(X'E(Y)) etc.
 
Physics news on Phys.org
Not too sure about the vector examples, but for the first couple: Always deal with each expectation in turn. For example if E(X) = 4, E(E(x)) = E(4) = 4. The rules of expections should prove very useful as well, like taking constants outside the expectation sign.
 

Similar threads

Undergrad Is this conditional expectation identity true?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Help understanding conditional expectation identity
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Statistical modeling and relationship between random variables
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Expected value of X~Geom(p) given X+Y=z
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Proof request for best linear predictor
  • · Replies 1 ·
Replies
1
Views
3K
MHB Distribution, expected value, variance, covariance and correlation
  • · Replies 14 ·
Replies
14
Views
2K
MHB Counterfactual Expectation Calculation
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Expectation of Product of three RVs
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How do E[X] and E[|X|] relate?
  • · Replies 6 ·
Replies
6
Views
1K
MHB Expected number of sold books and profit
  • · Replies 5 ·
Replies
5
Views
1K