MHB Chebyshev Inequality: Get Expert Help Now

  • Thread starter Thread starter nacho-man
  • Start date Start date
  • Tags Tags
    Inequality
Click For Summary
The discussion revolves around the application of Chebyshev's inequality, which states that for a random variable X with mean μ and variance σ², the probability that X deviates from μ by at least k is bounded by σ²/k². In this specific case, the variance is given as σ² = 9 and k = 3, leading to the conclusion that the probability P is less than or equal to 1. This implies that the complement, 1 - P, is non-negative. The conversation emphasizes the importance of understanding Chebyshev's inequality for probability assessments. Overall, the thread seeks clarification on applying this statistical principle to a given problem.
nacho-man
Messages
166
Reaction score
0
Could I get some help with this question?
Please refer to the attachment.

Thanks
 

Attachments

  • chebyshev.jpg
    chebyshev.jpg
    6.4 KB · Views: 84
Physics news on Phys.org
nacho said:
Could I get some help with this question?
Please refer to the attachment.

Thanks

The Chebysheff inequality extablishes that for a r.v. X with mean $\mu$ and variance $\sigma^{2}$ for $k \ge 0$ is...

$\displaystyle P \{|X - \mu| \ge k \} \le \frac{\sigma^{2}}{k^{2}}\ (1)$

In Your case is $ \sigma^{2}= 9$ and $k = 3$, so that the (1) supplies $\displaystyle P \le 1 \implies 1 - P \ge 0 $... an 'information' we have independently from Mr Chebysheff (Emo)...

Kind regards

$\chi$ $\sigma$
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
View full post »

Similar threads

High School Chebyshev inequality, confidence intervals, etc
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad On Jensen's inequality for conditional expectation
  • · Replies 1 ·
Replies
1
Views
2K
MHB Prove AM-GM Inequality: What Values to Use?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Are There Any Theorems Relating Joint Distributions to Marginals?
  • · Replies 7 ·
Replies
7
Views
3K
High School Bunkbed Conjecture Debunked?
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Bohmian Prediction of Bell Inequality Violations
  • · Replies 45 ·
2
Replies
45
Views
5K
MHB Properties of the Ordinals ....
  • · Replies 1 ·
Replies
1
Views
1K
MHB Prove the minimum and maximum edges in a graph
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad What Are the Benefits of Triangle Inequality in Mathematics?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Well Orders and Total Orders .... Searcoid Definition 1.3.10 ....
  • · Replies 5 ·
Replies
5
Views
2K