How Do You Compute E(f(x)) for Uniformly Distributed Variables?

  • Context: Undergrad 
  • Thread starter Thread starter tuanle007
  • Start date Start date
  • Tags Tags
    Stuck
Click For Summary
SUMMARY

To compute E(f(x)) for uniformly distributed variables, specifically when x is uniformly distributed between 0 and A, the formula is 1/A times the integral from 0 to A of f(x). In this discussion, A is defined as π and x as θ. The second part of the question, regarding the middle expectation, is contingent upon the values of k and m, indicating that it is wide sense stationary if it depends solely on the difference k-m rather than the individual values of k and m.

PREREQUISITES
  • Understanding of uniform distribution and its properties.
  • Familiarity with integral calculus.
  • Knowledge of wide sense stationarity in stochastic processes.
  • Basic concepts of expectation in probability theory.
NEXT STEPS
  • Study the properties of uniform distribution in detail.
  • Learn about integral calculus techniques for computing expectations.
  • Research wide sense stationarity and its implications in signal processing.
  • Explore examples of E(f(x)) calculations with different functions f(x).
USEFUL FOR

Students and professionals in mathematics, statistics, and engineering fields, particularly those working with probability distributions and stochastic processes.

tuanle007
Messages
35
Reaction score
0
Untitled.jpg


can someone please help me with this question. i don't know how to do this.
 
Physics news on Phys.org
To get E(f(x)) where x is uniformly distributed between 0 and A, you simply compute:
1/A integral from 0 to A of f(x). In your case A=pi and x=theta. This will give you the answers you need for (a).
The answer to (b) depends on the answer to the middle expectation. It will be a function of k and m. It is wide sense stationary if it is a function only of k-m, and not of them individuallly.
 

Similar threads

Undergrad How do E[X] and E[|X|] relate?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Failure rate for a uniformly distributed variable
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How Is the CDF Expressed for a Uniform Distribution on a Circle?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad How to Express Non-regular Prior Distributions by Mathematical Formula
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to show these random variables are independent?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Probability of White Ball in Box of 120 Balls: Solved!
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Relating Moments from one Distribution to the Moments of Another
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Probability paradox: P(X=x)=1/n >1
  • · Replies 5 ·
Replies
5
Views
3K
High School Continuous uniform distribution - expected values
  • · Replies 3 ·
Replies
3
Views
2K
MHB Distribution and Density functions of maximum of random variables
  • · Replies 6 ·
Replies
6
Views
5K