Understanding Chebychevs Inequality

  • Thread starter Thread starter Mary89
  • Start date Start date
  • Tags Tags
    Inequality
AI Thread Summary
Chebyshev's inequality states that for any random variable, the probability that it deviates from the mean by more than k standard deviations is at most 1/k^2. In the expression P[|x-mu|>=ksigma], x represents the random variable, mu is the mean, and sigma is the standard deviation. To find the probability that a<x<b using this inequality, one must express a and b in terms of standard deviations from the mean. Understanding this relationship helps clarify how Chebyshev's inequality can be applied to specific ranges. The discussion highlights the importance of grasping the concepts of mean and standard deviation in probability assessments.
Mary89
Messages
4
Reaction score
0
Hi, I am having trouble understanding Chebychevs inequality.

when it states P[|x-mu|>=ksigma]<=1/k^2, I don't really get what x-mu represents, For example if I wanted to know the probability that a<x<b, how would I use the inequality?

would I have to put a and b in terms of standard deviations?, is that what x-mu represents?

Thank you so much, anything that you can say about the inequality, even if it doesn't answer my specific question may help me to understand it better...
 
Physics news on Phys.org
Hey I got it!
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
View full post »

Similar threads

I On Jensen's inequality for conditional expectation
Replies
1
Views
2K
A A different discrete normal distribution
Replies
2
Views
2K
B Chebyshev inequality, confidence intervals, etc
Replies
6
Views
4K
I How to obtain moment bound from the importance sampling identity?
Replies
1
Views
2K
I What Are the Benefits of Triangle Inequality in Mathematics?
Replies
2
Views
2K
A Why the triangle inequality is greater than the 2 max{f(x),g(x)}
Replies
1
Views
1K
MHB Probability to get a chocolate snowman or a chocolate reindeer
Replies
2
Views
2K
I Question about convex property in Jensen's inequality
Replies
4
Views
2K
MHB Probability that the total annual profit is not more than 800000
Replies
6
Views
3K
B What Are Basic Questions About Understanding Inequalities?
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top