# dice - "Fair Dice Example of MaxEntropy observed mean of...

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"Fair" Dice - Example of MaxEntropy observed mean of draws muh 3.40 Sides of the Dice z 1 2 3 4 5 Posterior-Distribution p 0.18 0.18 0.17 0.16 0.16 Calculation of the Entropy and the Data Constraints Constraints: Sum over j = muh 0.18 0.35 0.51 0.65 0.79 Calculation of Entropy 0.31 0.31 0.30 0.30 0.29 1 2 3 4 5 0.00 0.05 0.10 0.15 0.20 0.25 discrete Probability Density Function Sides of the Dice relative Frequency, p

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6 0.15 Sum(p) 1.00 0.92 M 3.40 0.29 H 1.79 6
0.17 0.17

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0.17 0.17 0.17 0.17
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 Entropy as funtion of different means of the dice experiment Observed Mean m Entropy H

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1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 Probability of each of the six support points as a function of observed mean m Side 1 Side 2 Side 3 Side 4 Side 5 Side 6 Prob.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 ntropie und Normalized Entropie für verschiedene Mittelwerte des Würfelexperiment Mittelwert m Entropie H

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Side 1 Side 2 Side 3 Side 4 Side 5 Side 6 1 1 1.1 0.91 0.08 0.01 6.83E-04 6.15E-05 2.54E-06 1.2 0.83 0.14 0.02 0 6.44E-04 1.07E-04 1.3 0.77 0.18 0.04 0.01 0 5.09E-04 1.4 0.71 0.21 0.06 0.02 0.01 0 1.5 0.66 0.22 0.08 0.03
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## This note was uploaded on 08/01/2008 for the course ARE 213 taught by Professor Imbens during the Spring '06 term at Berkeley.

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dice - "Fair Dice Example of MaxEntropy observed mean of...

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