How can I improve my understanding of Maximum Likelihood estimators?

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SUMMARY

The discussion focuses on improving understanding of Maximum Likelihood Estimators (MLE) specifically for a continuous random variable X with the probability density function (pdf) f(x;theta)=theta(1+theta)x^(theta-1)(1-x). The key equation derived is (theta)^2 + (2+a)theta + 1 = 0, where 'a' is a parameter that needs clarification. Participants are encouraged to specify their difficulties and enhance their notation for better comprehension.

PREREQUISITES
  • Understanding of Maximum Likelihood Estimation (MLE)
  • Familiarity with probability density functions (pdf)
  • Basic knowledge of continuous random variables
  • Ability to solve quadratic equations
NEXT STEPS
  • Study the derivation of Maximum Likelihood Estimators in statistical theory
  • Learn about the properties of probability density functions
  • Explore the implications of parameter 'a' in MLE equations
  • Practice solving quadratic equations in the context of statistical estimators
USEFUL FOR

Statisticians, data scientists, and students seeking to deepen their understanding of Maximum Likelihood Estimators and their applications in statistical modeling.

benji84
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Can anyoe help with likelihood estimtor problems?
:cry:
 
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It goes like this:

Let X be a continuous r.v with pdf:

f(x;theta)=theta(1+theta)x^(theta-1).(1-x)

Show that the maximum likelihood estimator of theta satisifies:

a.(theta)^2+ (2+a)theta+1=0
 
What is 'a'? What values is f nonzero for? And be clearer with your notation please. Also, where are you having trouble?
 
Last edited:

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