How can I improve my understanding of Maximum Likelihood estimators?

Thread starter benji84
Start date Apr 17, 2005
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Estimators Likelihood Maximum Maximum likelihood

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To improve understanding of Maximum Likelihood Estimators (MLE), it's essential to clarify the problem involving the continuous random variable X with the given probability density function (pdf). The task is to show that the maximum likelihood estimator of theta satisfies the quadratic equation (theta)^2 + (2+a)theta + 1 = 0, where 'a' needs to be defined. Participants are encouraged to specify where they encounter difficulties and to use clearer notation for better comprehension. Additionally, it's important to identify the values for which the pdf f(x;theta) is nonzero. Engaging with these elements will enhance the grasp of MLE concepts.

Apr 17, 2005

benji84

Can anyoe help with likelihood estimtor problems?
:cry:

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Apr 17, 2005

benji84

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

Apr 17, 2005

BicycleTree

What is 'a'? What values is f nonzero for? And be clearer with your notation please. Also, where are you having trouble?

Last edited: Apr 17, 2005

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