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N coins have probability $p_n = e^{-t_n/s}$ of heads, $t_n$ being specific for each coin. Coins 1 to m came up heads and m+1 to N came up tails. Now I'm trying to estimate $s$ using the Maximum Likelihood Method.

$L(s) = p_1 p_2 \dots p_m (1-p_{m+1})\dots(1-p_N)$

But this function is difficult to maximize. Do I have to resort to numerical methods?

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it may be important, how do t_n grow and how small is m/N –  Fedor Petrov Dec 2 '10 at 13:12
Fedor: Both are unknown. This is actually a model of memory, where $t_n$ is the interval between successive reminders and $m$ is the number of tims the item was remembered. –  user7946 Dec 2 '10 at 13:48
seems like $s\to \infty$ and that the likelihood might not take on its maximum. –  Suvrit Jan 2 '11 at 21:32

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