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I think you start by working the maximum likelihood estimation formula of a binomial RV. The number of photons captured is (1,000,000) and the probability of the camera catching a photon is p, n (the number of photons total) is what we are looking for.
 
I think you start by working the maximum likelihood estimation formula of a binomial RV. The number of photons captured is (1,000,000) and the probability of the camera catching a photon is p, n (the number of photons total) is what we are looking for.
  
<math>\hat n_{ML} = \text{max}_n ( \binom{n}{k} ) = |x_i|</math>
+
<math>\hat n_{ML} = \text{max}_n ( \binom{n}{k} p^{k} (1-p)^{n-k} )</math>

Revision as of 10:22, 10 November 2008

I think you start by working the maximum likelihood estimation formula of a binomial RV. The number of photons captured is (1,000,000) and the probability of the camera catching a photon is p, n (the number of photons total) is what we are looking for.

$ \hat n_{ML} = \text{max}_n ( \binom{n}{k} p^{k} (1-p)^{n-k} ) $

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood