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April 2017 Q 9 (iii) CT6 Acceptance Rejection Method

M

mcallist

Member
Hi,

In this question we need to find the value of Beta that makes the algorithm as efficient as possible by finding the value that maximises 1/C. Since this is the same as minimising C. Then, in the solution, to find the minimum value of C, we take logs and differentiate the same way as when we're looking for a maximum. It's only when we differentiate the second time that we confirm that it is a minimum.

Are we meant to know this before or just assume that the solution will be correct. I don't get how when we're looking for a minimum, we just go about it the same way as when we're looking for a max. Could someone please explain this or if I'm missing something really obvious.

Thanks,
Tom
 
The log is a monotonic increasing function. So if we find when the maximum or the minimum of the log of the function occurs then it will be exactly the same as when the maximum or minimum of the original function occurs.

It is not specific only to maxima.
 
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