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mu of 0, sigma of
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11.952330.578540.230685.797670.901405.707670.37847214.38
5030.518251.324460.153052.223770.786771.900441.833151.85
6012.121971.66716318.138241.320882.363003.116370.422004.
514273.031600.377460.987541.698630.30650413.149700.26555
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0703.590670.860500.34349138.830111.023790.172741.332150.
547720.394080.538051.226452.169410.614900.810831411.9536
00.995701.806614.523930.184950.573560.308130.841640.6238
61.404450.690761512.004932.206141.273181.287650.715950.3
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916.835870.060773.041710.522641.116522.712350.637332.913
284.669200.558980.603092016.816650.628970.426272.160680.
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2202.867481.271720.266291.012050.607070.457560.355532.53
448
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20.403711305996428 14.385033836544503
18.138238812146792 13.149697549699873
24.870820924279094 8.6742243105807528
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mu of 1, sigma of
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860.0985331.1857161.1051211.3520914.4176010.294502.35924
290.633600.476652.822485.698180.3823674.584280.821851.04
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144.92661157466219 90.633602909716274
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203.7876046424858 86.354849172195856
mu of 3, sigma of
1.5mu0sigma112345678910nsum1575.16790185.6011366.37201
36.8848734.8631854.1685810.7236486.0321310.8952972.86025
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5778…
Excel_DataTablesHistogramsDistributions.xlsx
HistogramSet F to the number of random draws that you with to
sum together.You can observe the distribution that emerges on
the right.At F=1, you see that values are just uniformly
distributed.At F=12, you can clearly see the normal distribution
emerge out of
randomness.F12F_Row123456789101112BinsCDFPDFnSum000
017.55777842530.87562150530.53060700020.60952199240.428
41704640.48193827180.7891559950.12647899340.5313854892
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49526340.0750216486
0.0 0.0 0.0 0.0 0.0 1.0 3.0 9.0 19.0 19.0 16.0 19.0
10.0 4.0 0.0 0.0 0.0 0.0 0.0 0.0
DataTable1DSet F to the number of random draws that you with
to sum together.You can observe the distribution that emerges
on the right.At F=1, you see that values are just uniformly
distributed.At F=12, you can clearly see the normal distribution
emerge out of
randomness.F12F_Row123456789101112BinsCDFPDFn6.59652
67558000015.19383833850.04245923980.14376956830.970774
71310.6162954320.71686897430.78614679790.22771558690.94
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640.050.60026.98548528570.11.20036.56123479210.151.80045.
65198431390.22.40055.89310811590.2530064.97169823380.33.
60275.92108070870.354.221284.74006038050.44.8142496.0413
0214870.455.43823105.04925015790.566118116.49069879270.
556.67912127.11838383250.67.2916136.10493683560.657.8973
144.28810391190.78.41000155.01552716310.7591000166.0905
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020973294.6625617202305.6256813159315.6657690847326.08
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6.0 3.0 0.0 0.0 0.0 0.0 0.0 0.0
FindMuSigmaMu300Sigma100Likelihood-
7526.0947375881mu100300sigma5100p(Data1)Data1DataTest0.
0004974637195.9471026793239.1912645756-
57500750000.00054448572100.4224408589170.0259416762-
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195157101951014001600.00052091821098.2175013529158.170
997143-
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0002117.520.000628084619107.7123551982253.040800097841
201000012000.00052391442098.5019379672364.62366614794.
5122.510000122.500.00048476022194.6832896991417.3950685
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676-5-20000-
20000.000628833923107.77436777267.6690128481-4.5-15000-
15000.000633528824108.1617122405247.6901562516-4-10000-
10000.000574606325103.1387913876336.304070098-3.5-5011-
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3021010.00050116782796.3109753955166.6067716579-
2.550645040.00051183892897.3479913453352.5890648802-
21002115100150.000572085129102.9155483653297.853182066
6-
1.51505534150340.00052167233098.2892013184324.22042467
07-
120014994200940.00049435763195.6403791837358.396576723
1-
0.52502831342501340.00048260123294.466003387224.526134
803203004852023002020.00049394453395.5994815907319.346
29966030.53506761913501910.00049720943495.922048149840
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1087418.48341295770.00046603037892.7730123529332.99674
237580.000527351779

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