Why we find expectation value?

Click For Summary
SUMMARY

The discussion centers on the concept of expectation value in probability theory and statistics. Expectation value is defined as the average outcome of a random process, calculated using the probability distribution of the outcomes. As the number of repetitions of an experiment increases, the mean value of the outcomes converges to the expectation value, confirming its accuracy. This principle is fundamental in understanding random processes and predicting average results.

PREREQUISITES
  • Understanding of probability distributions
  • Familiarity with statistical mean and variance
  • Knowledge of random processes
  • Basic concepts of experimental repetition
NEXT STEPS
  • Study the properties of probability distributions
  • Learn about the Law of Large Numbers
  • Explore the Central Limit Theorem
  • Investigate applications of expectation value in statistical analysis
USEFUL FOR

Students in statistics, data analysts, and researchers involved in probabilistic modeling and experimental design will benefit from this discussion.

rida
Messages
13
Reaction score
0
why we find expectation value?

why do we take expectation value of sime entity? and how come we know that our expected value is correct
 
Physics news on Phys.org
If you have a random process which generates experimental outcomes, you cannot predict the individual outcome. If you know the probability distribution, you can however calculate what you will get on average. This is the expectation value.

If you average the outcomes of many repetitions of the experiment, you get the mean value. This mean value converges to the expectation value if you increase the number of repetitions.
 
  • Like
Likes   Reactions: 1 person

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K