- Thread starter alkiii321
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\(\displaystyle \text{Let }o = \text{#1's in }\bar{x},~s=\text{#6's in }\bar{x}\)

\(\displaystyle p_\epsilon(\bar{x}) = \left(\dfrac 1 6\right)^{n-o-s}\left(\dfrac 1 6 - \epsilon \right)^s \left(\dfrac 1 6 + \epsilon\right)^o\)

\(\displaystyle \log(p_\epsilon(\bar{x}) = (n-o-s)\log\left(\dfrac 1 6\right) + s \log\left(\dfrac 1 6 - \epsilon\right) + o \log\left(\dfrac 1 6 + \epsilon\right)\)

The maximum likelihood estimate will result from minimizing this expression over \(\displaystyle \epsilon\)

This is done using the usual calculus minimization technique of setting the first derivative to zero and solving.

Can you finish?

If you don't know what an estimator is why have you been given this problem? (Maybe your school uses a different name.)I don't understand. What is an estimator?

An estimator is a function that takes a set of observations and reduces them to an estimate of some property of the underlying random variable.