M$-$Step

$3$ points possible $($graded$)$

Fixing $,$ we want to update such that our lower bound is maximized.

What is the optimal $?$ For simplicity, assume we only have two data points and for this particular question. Answer in terms of $,,$ and $,,$ which are defined to be

$($For ease of input, use subscripts instead superscripts, i$.$e$.$ type x$\_$i for $.$ Type gamma$\_$ki for $.)$

unanswered

What is the optimal $?$ Answer in terms of $,,$ and $,$ which are defined as above to be $,$ and $.$

$($Type hatmu$\_$k for $.$ As above, for ease of input, use subscripts instead superscripts, i$.$e$.$ type x$\_$i for $.$ Type gamma$\_$ki for $.)$

unanswered

What is the optimal $?$ Answer in terms of and $,$ which are defined as above to be $,$

$($As above, type gamma$\_$ki for $.)$

Note: that you must account for the constraint that where $.$

Note: If you know that some aspect of your formula equals an exact constant, simplify and use this number, i$.$e$..$