- #1
kungal
- 5
- 0
Homework Statement
I have
Code:
E(a) = 0, E(b) = x but E(|a+b|)=??Homework Equations
Any one know how I would go about determining E(|a+b|)?
Expectation of an absolute value
- Thread starter kungal
- Start date
Click For Summary
SUMMARY
The discussion centers on calculating the expectation of the absolute value of the sum of two random variables, specifically E(|a+b|), given that E(a) = 0 and E(b) = x, where x is a known positive constant. It is established that E(|a+b|) is at least as large as |E(a+b)|, which simplifies to |x| = x. The participants emphasize the importance of understanding the properties of expectation operators in this context.
PREREQUISITES- Understanding of expectation operators in probability theory
- Familiarity with random variables and their properties
- Knowledge of basic inequalities in statistics, such as the triangle inequality
- Concept of absolute values in mathematical expressions
- Study the properties of expectation operators in probability theory
- Learn about the triangle inequality and its applications in statistics
- Explore the concept of moment generating functions for random variables
- Investigate the implications of Jensen's inequality in relation to expectations
Students in statistics or probability theory, mathematicians focusing on expectation calculations, and anyone interested in understanding the properties of random variables and their expectations.
Similar threads
- · Replies 2 ·
- · Replies 1 ·
- · Replies 2 ·
- · Replies 10 ·
- · Replies 12 ·
- · Replies 1 ·
- · Replies 4 ·
- · Replies 5 ·