Using MINITAB, generate observations from an Exponential (lambda=1) distribution

Question

Using MINITAB, generate observations from an Exponential (lambda=1) distribution. Generate 200 samples of 30 observations each by generating 200 rows of data and storing the results in columns C1-C30. Refer to the MINITAB Instructions provided at the end of the. assignment. i. Now, to simulate a random sample of size n = 3, select data from columns C1 - C3. Find the mean row-wise and store the result in column C31. ii. Similarly, simulate a random sample of size n = 10 by selecting data from columns C1-C10. Find the-mean row-wise and store the result in column C32 iii. Finally, simulate a random sample of size n = 30 by selecting data from columns C1-C30. Find the-mean row-wise and store the result in column C33. a) Plot a histogram of the sample means obtained in each of ii) and iii), and describe the shape of the distribution for each case. What do you notice as the sample size increases? b) What theoretical result is illustrated by this procedure?

Explanation / Answer

MTB > Random 200 c1-c30;
SUBC>   Exponential 1.0.
MTB > RMean C1-C3 c31.
MTB > RMean C1-C10 c32.
MTB > RMean C1-C30 c33.
MTB > print c31-c33

Data Display

Row      C31      C32      C33
1 0.56288 1.15187 1.10389
2 1.81632 0.95770 0.80870
3 2.64169 1.56964 1.07324
4 1.37089 0.90176 0.89976
5 1.86750 1.26990 1.22837
6 0.59963 0.99248 0.94813
7 1.17640 0.78774 1.06698
8 0.41934 1.03097 0.99192
9 0.72045 0.54891 0.99749
10 0.29677 0.94516 1.16608
11 0.75323 0.99359 0.94610
12 0.47267 1.08559 1.28016
13 1.15921 0.62844 0.99159
14 1.02636 0.94878 0.97302
15 0.40758 1.01624 0.96048
16 0.92803 1.04790 1.05098
17 0.27538 1.15305 1.28985
18 0.69697 0.72669 0.89787
19 0.57623 1.17461 0.95864
20 0.73568 1.49274 1.12836
21 1.24032 1.06025 1.05137
22 0.73070 0.77133 0.78967
23 1.69506 1.49941 1.29116
24 1.06527 1.01710 0.89424
25 0.51099 0.85906 0.93979
26 1.34244 0.93611 0.94257
27 1.18952 1.14100 1.17691
28 0.94873 1.03836 0.96401
29 0.83376 0.79846 0.80511
30 0.57045 1.53402 0.93602
31 1.94747 1.07294 1.15424
32 0.53293 1.27391 1.42413
33 0.92554 0.88500 0.97902
34 1.29350 1.09355 0.76101
35 0.73282 0.98268 0.99764
36 0.87021 0.78041 0.75136
37 1.36967 0.97154 1.25115
38 0.39611 0.88128 0.70632
39 0.76360 0.89139 0.91749
40 0.14011 0.85264 0.96621
41 0.72762 0.81235 0.78356
42 1.42865 1.50792 1.01092
43 0.57641 0.73595 0.80586
44 1.33240 0.98954 1.12262
45 0.52221 1.05742 0.91279
46 0.50160 0.63259 0.96057
47 1.09938 0.81033 1.10527
48 0.35326 0.66332 0.68114
49 0.85625 1.43070 1.04163
50 0.70133 1.14021 1.26146
51 1.08192 0.59108 0.66074
52 0.51516 0.98220 1.04943
53 0.38318 0.38058 0.79747
54 1.20075 1.17391 1.03533
55 1.49077 1.12422 1.04749
56 0.48935 0.81249 0.90415
57 1.39481 0.94434 0.90835
58 0.42270 0.49254 0.94852
59 0.59978 0.79509 0.84961
60 1.16529 0.83592 0.88996
61 0.73758 0.62093 0.99396
62 1.44753 0.91719 1.13490
63 0.68848 0.93084 0.81597
64 0.47556 0.60127 1.14081
65 1.21857 0.84393 0.84809
66 2.61361 1.55698 1.26202
67 1.31858 1.24776 1.19175
68 1.80716 1.05879 1.20049
69 0.62074 1.05746 1.09467
70 0.88477 0.91517 0.77823
71 0.95305 1.15706 0.89679
72 1.22207 1.31983 1.00528
73 0.33972 0.77281 0.97322
74 1.05597 0.95018 0.94274
75 1.04586 1.45567 1.13032
76 0.79796 0.45836 0.90236
77 0.50593 1.08287 0.75635
78 1.12238 0.68047 1.02308
79 1.64211 1.05071 0.85602
80 0.57885 1.07203 1.33233
81 1.24547 0.89208 1.45339
82 0.75616 1.26285 1.04488
83 0.15136 0.38308 0.77740
84 1.42079 1.23635 0.90745
85 0.57429 1.41492 1.04059
86 0.49173 0.91205 0.87453
87 1.49551 1.12338 1.12034
88 0.72046 1.34093 1.30024
89 0.22104 0.45363 1.01713
90 0.84115 0.74276 1.03891
91 0.19907 0.82214 0.83947
92 1.40236 1.41807 0.80884
93 0.67695 0.70496 0.89644
94 1.27849 1.63469 1.35664
95 0.39096 0.69429 1.02148
96 0.69687 0.99760 1.20386
97 0.70695 1.15681 0.98660
98 0.61521 0.77754 0.92059
99 0.99467 1.39605 1.13162
100 0.73474 1.21801 0.80759
101 0.57588 0.84826 0.98457
102 1.99006 1.44535 0.98234
103 0.67591 0.78293 0.87930
104 0.52058 1.73010 1.00449
105 0.92220 0.97571 1.08811
106 1.25749 1.42640 1.20483
107 1.09146 1.06493 1.02761
108 0.68636 0.87993 1.00228
109 0.74711 0.67749 0.69905
110 2.23141 1.03874 0.87365
111 0.65714 0.75176 0.89589
112 1.06482 0.79181 0.86626
113 0.79554 0.83039 1.03619
114 2.51975 1.48558 1.08911
115 1.09071 0.95338 1.01965
116 0.89889 0.81014 1.07589
117 0.95890 1.16127 0.89178
118 0.59492 1.12378 1.11588
119 0.63477 1.00703 0.95791
120 0.90673 1.01733 0.68230
121 2.04588 1.41968 1.41876
122 1.76661 1.12495 1.40426
123 0.52363 0.51224 0.85296
124 0.63538 1.29806 0.88561
125 0.23978 1.78018 1.24452
126 1.04283 1.11393 1.12119
127 0.13054 0.62227 0.75851
128 1.48665 0.82905 0.97234
129 1.09136 1.29377 1.24569
130 0.84060 1.00369 1.09186
131 1.08817 1.14214 0.80890
132 1.53738 1.15966 0.76281
133 1.01156 1.21700 1.28164
134 2.23073 1.50356 1.67052
135 0.97749 0.68164 0.65760
136 0.64350 1.03653 0.96237
137 2.66277 1.42542 1.17871
138 0.67775 0.86357 0.95627
139 2.09170 1.24061 0.97559
140 0.24449 0.80034 0.87420
141 1.53833 1.05378 0.86727
142 0.62892 0.49480 0.91691
143 0.55174 0.82037 0.77533
144 0.73549 1.39797 1.01907
145 0.59551 0.38293 0.89390
146 1.03030 0.95999 0.85680
147 0.59754 1.84841 1.28748
148 1.36006 1.25284 0.89291
149 1.60922 1.30791 1.00984
150 1.02962 1.11321 0.87303
151 0.55983 1.06599 0.99706
152 0.82461 1.50457 1.47395
153 0.54956 0.72876 0.70612
154 1.15498 0.78796 1.00227
155 0.62836 1.54098 1.52005
156 0.82638 0.52970 0.77447
157 1.46067 1.25634 1.19047
158 0.76219 0.66998 0.86447
159 1.18377 1.20141 1.03564
160 1.87648 1.12087 1.31591
161 0.90372 0.89050 1.16526
162 0.68525 0.91508 0.90462
163 1.94250 1.20618 1.48309
164 1.84776 1.26078 1.20046
165 1.46446 1.38214 1.26607
166 2.04192 0.82622 0.97624
167 0.46562 0.49375 0.90700
168 0.78107 0.58784 0.64713
169 0.80281 0.83208 1.08992
170 1.03699 1.07731 0.91672
171 1.54709 0.93648 1.10466
172 0.64576 1.36738 1.29415
173 1.27586 1.03137 0.87599
174 2.81372 1.04200 1.07315
175 0.52563 0.98105 0.89926
176 0.39136 0.56338 0.73435
177 1.36347 0.84400 0.99726
178 0.38794 0.79511 0.70720
179 1.17764 0.91620 1.15396
180 0.83994 1.21450 1.23964
181 1.62726 1.16872 0.86878
182 0.36534 0.60546 0.84381
183 0.40966 0.69260 0.74754
184 0.38953 1.18662 1.12906
185 1.38266 0.89522 1.01682
186 1.23070 0.94702 1.29326
187 1.57074 1.21582 1.47265
188 0.70136 0.81096 0.90215
189 1.35987 1.19847 1.06350
190 1.02144 1.25219 1.03913
191 0.58912 1.12204 1.15369
192 0.62287 0.84037 1.03260
193 0.16136 0.47340 0.83828
194 0.33595 0.74990 0.82628
195 0.72020 0.94146 1.11323
196 0.41708 0.46148 0.58224
197 0.61749 1.05685 0.96661
198 1.11293 0.70703 0.77675
199 1.32046 1.17555 0.92422
200 0.80380 0.40884 0.60187

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