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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 24 December 7, 2010 1. A blackbody at temperature radiates photons of all wavelengths, described by its characteristic spectrum. This problem will have you estimate , which is fixed but unknown. The PMF for the number of photons K in a given wavelength range and a fixed very short time interval is given by, p K ( k ; ) = 1 Z ( ) e- k/ , k = 0 , 1 , 2 , ... Z ( ) is a normalization factor for the probability distribution (the physicists call it the partition function). You are given the task of determining the temperature of the body to two significant digits by photon counting in non-overlapping time intervals of duration one second. The photon emissions in non-overlapping time intervals are statistically independent from each other....
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