I understand why (D) is one of the answers but i dont know about the rest?
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2$\begingroup$ One approach would be to compute the likelihoods for all four estimators. Another is to compute the maximum likelihood estimate outright. Have you tried either of these? $\endgroup$– whuber ♦Commented Feb 8, 2019 at 17:43
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2$\begingroup$ Please add the 'self-study' tag and read the tag wiki. $\endgroup$– StubbornAtomCommented Feb 8, 2019 at 18:17
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2$\begingroup$ If any statistic $T$ such that $T_1<T<T_2$ is an MLE, then $\alpha T_1+(1-\alpha)T_2$ is also an MLE for any $\alpha\in(0,1)$ since it lies between $T_1$ and $T_2$. As option (D) is correct, check if you can write the estimators in options (A),(B),(C) in the form $\alpha(\frac{Y_n-1}{2})+(1-\alpha)(\frac{Y_1+1}{2})$. $\endgroup$– StubbornAtomCommented Feb 11, 2019 at 9:46
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