Find the Maximum Likelihood Estimator from the Probability Mass Function Statistics

Описание: Statistics and Bayesian Statistics and Point Estimation.
This Video shows how to find the candidate for the Maximum Likelihood Estimate of theta from a set of discrete observations for P(X=x) which is the probability mass function.
We take the product of all these probability mass function given observations.
The product is then factored to show all the theta in similar format grouped together, this is our Likelihood function.
Next, we find the log likelihood function with respect to theta. This will be easier to differentiate in the next few stages.
The log likelihood is then differentiated with respect to theta, and we set l'(theta)=0.
This gives us our candidate for the MLE of theta. also, known as hat theta.
To check if this is a suitable candidate, we take the second derivative of the log likelihood function and see that it is less than zero always. If so, it is a suitable candidate.

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