O: "Solving Chi Square Problems: E(s^2) and Var(s^2) Using MLE

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SUMMARY

The discussion focuses on solving Chi Square problems, specifically finding the expected value E(s²) and variance Var(s²) using Maximum Likelihood Estimation (MLE). The key equations referenced include E(W) = v and Var(W) = 2v, where W is defined as W = vS²/σ², distributed as X²_v. The participants emphasize the application of MLE for variance estimation, clarifying that Var(s²) does not equal σ² directly but can be derived through proper application of statistical principles.

PREREQUISITES
  • Understanding of Chi Square distribution
  • Familiarity with Maximum Likelihood Estimation (MLE)
  • Knowledge of expected value and variance calculations
  • Basic statistical concepts related to random variables
NEXT STEPS
  • Study the derivation of E(s²) and Var(s²) in Chi Square distributions
  • Learn about Maximum Likelihood Estimation (MLE) techniques for variance
  • Explore the properties of Chi Square distributions and their applications
  • Review statistical methods for estimating parameters of random variables
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Students and professionals in statistics, data analysis, and research who are working with Chi Square distributions and require a deeper understanding of variance estimation techniques.

dim&dimmer
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Homework Statement


W = \frac{vS^2}{\sigma^2}, distributed as X^2_v
Find E(s^2) and Var(s^2)

Homework Equations


E(W) = v , Var(w)=2v

The Attempt at a Solution


Have been trying to figure this out with no luck. Can I use MLE for variance to show Var(s^2)= \sigma^2? Really don't know how to get started on this, any pointers would be appreciated.
DIM
 
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Remember that for any random variable X and constant k

<br /> E(kX) = kE(X), \quad Var(kX) = k^2 Var(X)<br />
 
Thank you,
Sheesh, should have posted my question ...days ago, pretty simple really.
Dimmer.
 

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