Statistics- unbiased estimator

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SUMMARY

The discussion centers on determining the constant c in the statistic c(Y1 + 2Y2) to ensure it serves as an unbiased estimator for 1 / θ, where Y1 and Y2 are drawn from the probability density function fY(y; θ) = 2yθ² for 0 < y < 1/θ. The user initially struggled with calculating the expected value E[c(Y1 + 2Y2)] but ultimately reached a solution. The key takeaway is that setting the expected value equal to 1 / θ allows for the determination of c.

PREREQUISITES
  • Understanding of unbiased estimators in statistics
  • Familiarity with probability density functions (pdf)
  • Knowledge of expected value calculations
  • Basic concepts of random sampling
NEXT STEPS
  • Study the properties of unbiased estimators in statistical theory
  • Learn about calculating expected values for linear combinations of random variables
  • Explore the concept of maximum likelihood estimation
  • Investigate the implications of different probability distributions on estimators
USEFUL FOR

Statisticians, data analysts, and students studying statistical estimation methods will benefit from this discussion, particularly those focusing on unbiased estimators and probability theory.

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Homework Statement


A random sample of size 2, Y1 and Y2, is drawn from the pdf

fY(y;[tex]\vartheta[/tex])=2y*[tex]\vartheta[/tex]2, 0<y< 1/ [tex]\vartheta[/tex]

What must c equal if the statistic c(Y1+2Y2) is to be an unbiased estimator for 1 / [tex]\vartheta[/tex]

Homework Equations





The Attempt at a Solution



I tried to find the E[c(Y1+2Y2)] but don't really know how to reach 1 / [tex]\vartheta[/tex]

There is also the equation of the Ymax

maybe I should set them equal ? but how to get rid of Y1 and Y2 ?

Thanks.
 
Last edited:
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oh, I got it :\
 

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