ABCDEFGHIJKLMNOPQRS
1
2
RANDOM VARIABLE GENERATION
3
4
PARAMETERSEXPONENTIAL RANDOM VARIABLE GENERATIONHISTOGRAM PARAMETERSHISTOGRAM
5
ParameterDomainValue#Random~U[0,1]X~Exponential(lambda)MeasureValue#
Lower Bound
Upper Bound(LB+UB)/2
Absolute Frequency
Relative Frequency
Histogram Frequency
6
lambdaR+0,110,369371274,61037978Size1000010,00016,03923,019745810,45810,075856
7
20,9702838035,16062822Min0,000126,039212,07839,058825480,25480,042192
8
MEASURES30,8844353621,57925230Max90,5867312,078318,117415,097913230,13230,021907
9
MeasureData Measurements
Parametric Measurements
40,8379948018,20126843Bins15418,117424,156521,13707220,07220,011955
10
Mean9,786310,000050,8640383619,95382507Range6,0391524,156530,195627,17613550,03550,005878
11
Variance97,5899100,000060,8782348921,05661439630,195636,234733,21521950,01950,003229
12
Standard Deviation9,878810,000070,487224826,67917779736,234742,273839,25431240,01240,002053
13
Skewness2,05532,000080,9353604027,38928111842,273848,312945,2934700,00700,001159
14
Kurtosis8,99269,000090,507844577,08960692948,312954,352051,3325410,00410,000679
15
Median6,81736,9315100,019645580,198411221054,352060,391257,3716150,00150,000248
16
Mode0,00010,0000110,8315264117,809762511160,391266,430363,4107120,00120,000199
17
120,557705158,157785281266,430372,469469,449880,00080,000132
18
DATA MOMENTS130,491947756,771709731372,469478,508575,488950,00050,000083
19
k
Non Central Moments - µ'[k]
Central Moments - µ[k]140,109714531,162131141478,508584,547681,528000,00000,000000
20
19,78630,0000150,7358364413,311868231584,547690,586787,567110,00010,000017
21
2193,352697,5802160,7021130912,11041353
22
35783,56121981,4408170,9640787433,26426032
23
4228453,208385643,6711180,027018800,27390522
24
190,553075188,05364887
25
PARAMETRIC MOMENTS - ⚠️[No analytical formula] [∫Integration]200,345585814,24014812
26
k
Non Central Moments - µ'[k]
Central Moments - µ[k]210,276747933,23997471
27
19,98830,0000220,471723536,38135520
28
2198,810999,0449230,9866497843,16222401
29
35877,81711913,4569240,440323015,80395472
30
4227276,074981586,2627250,097368511,02440909
31
260,631376029,97978192
32
270,119401061,27152988
33
280,244727722,80676957
34
290,225053222,54960929
35
300,131902941,41451755
36
310,508492397,10277858
37
320,389337034,93210076
38
330,9832559940,89714496
39
340,614905419,54266282
40
350,364337034,53086773
41
360,9059799923,64247687
42
370,613093449,49572066
43
380,127073581,35904016
44
390,027950360,28348403
45
400,558816408,18294156
46
410,179095701,97348740
47
420,133518751,43314808
48
430,188651792,09057963
49
440,207511352,32577093
50
450,117299681,24769529
51
460,374047814,68481277
52
470,542830607,82701273
53
480,605652779,30523460
54
490,7050124812,20822244
55
500,9698810935,02601929
56
510,8845288321,58734352
57
520,9916196347,81863339
58
530,412236065,31429869
59
540,158041421,72024457
60
550,9398833728,11468851
61
560,064460850,66632282
62
570,306658893,66233174
63
580,7816189015,21513578
64
590,610008859,41631239
65
600,453946506,05038319
66
610,427284125,57365529
67
620,196341942,18581402
68
630,6706912411,10759503
69
640,591803808,96007342
70
650,316177943,80057535
71
660,567362588,37855261
72
670,392302004,98077227
73
680,9702528635,15022426
74
690,7034857412,15659959
75
700,624889439,80534450
76
710,9896309345,68927809
77
720,134307911,44225986
78
730,6777779111,32514261
79
740,8232796217,33186581
80
750,288875693,40908029
81
760,395911785,04035026
82
770,541951157,80779438
83
780,505426187,04058860
84
790,507814037,08898644
85
800,180822771,99454815
86
810,9543250230,86204700
87
820,112754981,19634098
88
830,585224908,80018834
89
840,123274801,31561673
90
850,8852380021,64894846
91
860,7008715312,06882139
92
870,066913010,69256845
93
880,508782877,10869037
94
890,381360544,80232630
95
900,021874320,22117111
96
910,158230541,72249105
97
920,432068105,65753768
98
930,123107941,31371370
99
940,216578032,44083817
100
950,186778872,06752208