questions - I) Using the New Markowitz Frontier MS-Excel file

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Sheet1

Dart # X-coordinate Y-coordinate Hit? Hit Count Pi
1 0.5599908817 0.8683279551 0 0 0
2 0.8662500991 0.3328307141 0 1 2
3 0.2616485918 0.1709622453 0 2 2.6666666667
4 0.9157154806 0.2593999004 0 3 3
5 0.9342493388 0.7332547767 0 3 2.4
6 0.1705891837 0.7153468835 0 4 2.6666666667
7 0.6041423313 0.0308281355 0 5 2.8571428571
8 0.4624592317 0.0503243927 0 6 3
9 0.9068573746 0.6087335475 0 6 2.6666666667
10 0.9822513685 0.9856549879 0 6 2.4
11 0.1339705535 0.3564779538 0 7 2.5454545455
12 0.1732007463 0.3774177403 0 8 2.6666666667
13 0.3597930579 0.842576836 0 9 2.7692307692
14 0.1544458044 0.0364371769 0 10 2.8571428571
15 0.5280222209 0.1054622933 0 11 2.9333333333
16 0.6965513896 0.9518319254 0 11 2.75
17 0.5788555996 0.7980976727 0 12 2.8235294118
18 0.9202208462 0.8606702635 0 12 2.6666666667
19 0.1863799924 0.5638841521 0 13 2.7368421053
20 0.230839358 0.1506906634 0 14 2.8
21 0.2922175368 0.4657816013 0 15 2.8571428571
22 0.4281874099 0.9417128119 0 15 2.7272727273
23 0.5086482238 0.6175014206 0 16 2.7826086957
24 0.7607143495 0.122133516 0 17 2.8333333333
25 0.2894665384 0.7050737901 0 18 2.88
26 0.9830882088 0.4646888735 0 18 2.7692307692
27 0.526295967 0.6743226884 0 19 2.8148148148
28 0.4918521189 0.9206299422 0 19 2.7142857143
29 0.0946948439 0.0533616459 0 20 2.7586206897
30 0.240452444 0.2598445098 0 21 2.8
31 0.6376722632 0.7020101222 0 22 2.8387096774
32 0.3325959756 0.6031465027 0 23 2.875
33 0.7163090803 0.4349926797 0 24 2.9090909091
34 0.5946655905 0.9902883913 0 24 2.8235294118
35 0.6757222655 0.5538926465 0 25 2.8571428571
36 0.3699630554 0.6168446163 0 26 2.8888888889
37 0.1165622882 0.4377111767 0 27 2.9189189189
38 0.3831501554 0.6057657493 0 28 2.9473684211
39 0.072783346 0.0323967567 0 29 2.9743589744
40 0.4963447904 0.9497226575 0 29 2.9
41 0.2588282753 0.0019056154 0 30 2.9268292683
42 0.4209882972 0.3008301718 0 31 2.9523809524
43 0.3928656922 0.3921049549 0 32 2.976744186
44 0.5958205413 0.7869951049 0 33 3
45 0.8324807621 0.2284061327 0 34 3.0222222222
46 0.8864545272 0.7413326679 0 34 2.9565217391
47 0.6336641489 0.5341314553 0 35 2.9787234043
48 0.4583430848 0.466910216 0 36 3
49 0.8936983075 0.9242078562 0 36 2.9387755102
50 0.7565656239 0.4002663973 0 37 2.96
51 0.0070819219 0.2493104159 0 38 2.9803921569
52 0.8133565037 0.9166518861 0 38 2.9230769231
53 0.8994240997 0.7895119252 0 38 2.8679245283
54 0.9660941999 0.4855790499 0 38 2.8148148148
55 0.9558379587 0.4523722078 0 38 2.7636363636
56 0.0991042679 0.801304269 0 39 2.7857142857
57 0.2855875348 0.675675886 0 40 2.8070175439
58 0.9914444628 0.0881449699 0 41 2.8275862069
59 0.6659509089 0.6409902828 0 42 2.8474576271
60 0.2304410556 0.9379238154 0 43 2.8666666667
61 0.3311331813 0.5367915316 0 44 2.8852459016
62 0.2821515885 0.7771123601 0 45 2.9032258065
63 0.6501230081 0.0400626182 0 46 2.9206349206
64 0.7447160171 0.4193130631 0 47 2.9375
65 0.3744928624 0.2436428769 0 48 2.9538461538
66 0.1838046622 0.2136166839 0 49 2.9696969697
67 0.2804127624 0.0794369001 0 50 2.9850746269
68 0.2498039517 0.7289556456 0 51 3
69 0.8350753754 0.6070193732 0 51 2.9565217391
70 0.8781164872 0.1852354578 0 52 2.9714285714
71 0.4258622919 0.4869643069 0 53 2.985915493
72 0.1157076187 0.63344992 0 54 3
73 0.6990255921 0.1716507635 0 55 3.0136986301
74 0.4333792608 0.7586210656 0 56 3.027027027
75 0.3050558475 0.5064247572 0 57 3.04
76 0.2801259036 0.6659032969 0 58 3.0526315789
77 0.4269393567 0.3522920391 0 59 3.0649350649
78 0.044765326 0.8810458922 0 60 3.0769230769
79 0.2218765662 0.4678671395 0 61 3.0886075949
80 0.8779934743 0.0187709093 0 62 3.1
81 0.3603086018 0.7755908005 0 63 3.1111111111
82 0.4893001294 0.3376473615 0 64 3.1219512195
83 0.6506596203 0.4976147637 0 65 3.1325301205
84 0.2259511996 0.4479878867 0 66 3.1428571429
85 0.0361133647 0.5857929054 0 67 3.1529411765
86 0.4849294891 0.5691600576 0 68 3.1627906977
87 0.2707867509 0.0300336742 0 69 3.1724137931
88 0.9581643204 0.6367137237 0 69 3.1363636364
89 0.5701991511 0.9084515003 0 69 3.1011235955
90 0.0906581649 0.9791931518 0 70 3.1111111111
91 0.4820291416 0.8215655628 0 71 3.1208791209
92 0.6551301824 0.8942913278 0 71 3.0869565217
93 0.9031126204 0.1250037531 0 72 3.0967741935
94 0.7918409686 0.5764100174 0 73 3.1063829787
95 0.6594449418 0.6547681825 0 74 3.1157894737
96 0.0401003144 0.461106464 0 75 3.125
97 0.6677374949 0.0969093825 0 76 3.1340206186
98 0.8798643727 0.3973547911 0 77 3.1428571429
99 0.3638473757 0.3231138783 0 78 3.1515151515
100 0.9842567723 0.1496476701 0 79 3.16
101 0.8495781248 0.0274792574 0 80 3.1683168317
102 0.2298274277 0.9404160655 0 81 3.1764705882
103 0.8416199868 0.3023337909 0 82 3.1844660194
104 0.5980361611 0.5676255168 0 83 3.1923076923
105 0.6891591756 0.0406906358 0 84 3.2
106 0.9087827312 0.1680664225 0 85 3.2075471698
107 0.4465461557 0.9460297643 0 85 3.1775700935
108 0.3508077045 0.9747447547 0 85 3.1481481481
109 0.7180342619 0.3677548258 0 86 3.1559633028
110 0.8782534776 0.2377371559 0 87 3.1636363636
111 0.9720257742 0.4554008806 0 87 3.1351351351
112 0.0239095312 0.8120280838 0 88 3.1428571429
113 0.2406585068 0.0482455404 0 89 3.1504424779
114 0.7286501392 0.768434473 0 89 3.1228070175
115 0.3778140565 0.0319556442 0 90 3.1304347826
116 0.3018031472 0.3139381156 0 91 3.1379310345
117 0.377415009 0.8936329141 0 92 3.1452991453
118 0.038158047 0.0111801526 0 93 3.1525423729
119 0.6773373982 0.2537812237 0 94 3.1596638655
120 0.5114147061 0.8225262575 0 95 3.1666666667
121 0.9892701204 0.7049860372 0 95 3.1404958678
122 0.8152805023 0.2709950743 0 96 3.1475409836
123 0.9109905074 0.6903173438 0 96 3.1219512195
124 0.6472852146 0.7460049938 0 97 3.1290322581
125 0.6183705847 0.3411092947 0 98 3.136
126 0.9379436293 0.1845898408 0 99 3.1428571429
127 0.1954189905 0.881895653 0 100 3.1496062992
128 0.5714787545 0.0873220503 0 101 3.15625
129 0.161414986 0.0570401815 0 102 3.1627906977
130 0.979156104 0.3369129875 0 102 3.1384615385
131 0.0998487084 0.9140713395 0 103 3.1450381679
132 0.181908716 0.7780852055 0 104 3.1515151515
133 0.2104137168 0.9799920831 0 104 3.1278195489
134 0.7123181355 0.1426727287 0 105 3.1343283582
135 0.2240467465 0.0404600842 0 106 3.1407407407
136 0.4760383321 0.5911114082 0 107 3.1470588235
137 0.2770687656 0.3654782439 0 108 3.1532846715
138 0.3630125651 0.6398133018 0 109 3.1594202899
139 0.9022414699 0.1867821706 0 110 3.1654676259
140 0.7638544581 0.1658259984 0 111 3.1714285714
141 0.0494758438 0.8197594242 0 112 3.1773049645
142 0.1777118018 0.1043419647 0 113 3.1830985915
143 0.6242634139 0.0092627053 0 114 3.1888111888
144 0.7057846231 0.4215284637 0 115 3.1944444444
145 0.1700353965 0.0792598842 0 116 3.2
146 0.3982155961 0.260693203 0 117 3.2054794521
147 0.3725653192 0.085778474 0 118 3.2108843537
148 0.3811005948 0.0044013425 0 119 3.2162162162
149 0.3445846624 0.5414603392 0 120 3.2214765101
150 0.3269478819 0.7560847421 0 121 3.2266666667
151 0.6955842629 0.7391020215 0 121 3.2052980132
152 0.1336065631 0.8971868136 0 122 3.2105263158
153 0.315398068 0.3619327455 0 123 3.2156862745
154 0.1453469762 0.5138989213 0 124 3.2207792208
155 0.6080438912 0.4425726469 0 125 3.2258064516
156 0.6821736758 0.7186819741 0 126 3.2307692308
157 0.2113698056 0.6240513017 0 127 3.2356687898
158 0.9592339425 0.0251082038 0 128 3.2405063291
159 0.3562670659 0.2180093541 0 129 3.2452830189
160 0.2773061687 0.9102782756 0 130 3.25
161 0.1817394329 0.2441860683 0 131 3.2546583851
162 0.7146872652 0.9858984047 0 131 3.2345679012
163 0.9547918271 0.2918759285 0 132 3.2392638037
164 0.4760242428 0.7598514475 0 133 3.243902439
165 0.5646701081 0.5527949462 0 134 3.2484848485
166 0.9695046659 0.5844455849 0 134 3.2289156627
167 0.452998101 0.0214939159 0 135 3.2335329341
168 0.7569320999 0.5264162036 0 136 3.2380952381
169 0.3189950721 0.3917456738 0 137 3.2426035503
170 0.4162339657 0.06856544 0 138 3.2470588235
171 0.2895844424 0.0417027668 0 139 3.2514619883
172 0.3451032152 0.8322869432 0 140 3.2558139535
173 0.3595911312 0.4080313328 0 141 3.2601156069
174 0.349944275 0.7864258166 0 142 3.2643678161
175 0.2117499596 0.5545299423 0 143 3.2685714286
176 0.2037997915 0.2414004214 0 144 3.2727272727
177 0.180367592 0.3783194822 0 145 3.2768361582
178 0.6976298292 0.1413931282 0 146 3.2808988764
179 0.5135004775 0.0272265174 0 147 3.2849162011
180 0.4651856632 0.2258063107 0 148 3.2888888889
181 0.7248813893 0.8444714128 0 148 3.270718232
182 0.542225241 0.7157645223 0 149 3.2747252747
183 0.5605654722 0.661536814 0 150 3.2786885246
184 0.1093339977 0.9467224872 0 151 3.2826086957
185 0.5952826144 0.5787968207 0 152 3.2864864865
186 0.6633444657 0.0628253054 0 153 3.2903225806
187 0.5642495582 0.4306450288 0 154 3.2941176471
188 0.2885232615 0.2216453009 0 155 3.2978723404
189 0.6260255756 0.8792533664 0 155 3.2804232804
190 0.8752448011 0.5670901405 0 155 3.2631578947
191 0.3457392393 0.7968349559 0 156 3.2670157068
192 0.8008040302 0.1147085526 0 157 3.2708333333
193 0.3741806177 0.7206659121 0 158 3.274611399
194 0.0776445954 0.4349533773 0 159 3.2783505155
195 0.9679195254 0.1878344122 0 160 3.2820512821
196 0.1133819847 0.4414672653 0 161 3.2857142857
197 0.822602982 0.5037267952 0 162 3.2893401015
198 0.1228011684 0.0370577372 0 163 3.2929292929
199 0.170282736 0.8928227452 0 164 3.2964824121
200 0.0345716037 0.1294828531 0 165 3.3
201 0.5327210489 0.9318867061 0 165 3.2835820896
202 0.3596535864 0.8318881091 0 166 3.2871287129
203 0.3130203286 0.9158143144 0 167 3.2906403941
204 0.3937390903 0.8573909415 0 168 3.2941176471
205 0.1793544993 0.3357048309 0 169 3.2975609756
206 0.0597924986 0.4792580894 0 170 3.3009708738
207 0.7047089012 0.2759353727 0 171 3.3043478261
208 0.4097176352 0.2917178008 0 172 3.3076923077
209 0.7042966647 0.2898930115 0 173 3.3110047847
210 0.0406569799 0.0114169565 0 174 3.3142857143
211 0.6148643588 0.371972369 0 175 3.317535545
212 0.8187326075 0.0356745818 0 176 3.320754717
213 0.3772896631 0.1740007406 0 177 3.323943662
214 0.1039954514 0.3987589521 0 178 3.3271028037
215 0.9952330077 0.1275078429 0 178 3.311627907
216 0.4313509681 0.7088718215 0 179 3.3148148148
217 0.2663351332 0.8457663915 0 180 3.3179723502
218 0.9462136339 0.707607829 0 180 3.3027522936
219 0.2667805159 0.343121233 0 181 3.3059360731
220 0.1817013782 0.1093526395 0 182 3.3090909091
221 0.9355051332 0.2808966277 0 183 3.3122171946
222 0.7202224771 0.9719534546 0 183 3.2972972973
223 0.116314845 0.1525416346 0 184 3.3004484305
224 0.1324734866 0.3314692411 0 185 3.3035714286
225 0.7600584943 0.9373467063 0 185 3.2888888889
226 0.9378657547 0.8189770487 0 185 3.2743362832
227 0.2408124719 0.1960090575 0 186 3.2775330396
228 0.6055563278 0.6221733997 0 187 3.2807017544
229 0.6582358039 0.7335197628 0 188 3.2838427948
230 0.0163485969 0.7253173251 0 189 3.2869565217
231 0.682467121 0.7177343348 0 190 3.29004329
232 0.6810754868 0.508589244 0 191 3.2931034483
233 0.3321086062 0.0478304178 0 192 3.2961373391
234 0.2357272836 0.1911602422 0 193 3.2991452991
235 0.1907990449 0.9952574781 0 193 3.285106383
236 0.4357769116 0.401901694 0 194 3.2881355932
237 0.8718525951 0.0610083253 0 195 3.2911392405
238 0.6968595351 0.8515531185 0 195 3.2773109244
239 0.8059060916 0.9027877627 0 195 3.2635983264
240 0.44218923 0.7808495518 0 196 3.2666666667
241 0.1031165124 0.6611447476 0 197 3.2697095436
242 0.5592363909 0.0602597468 0 198 3.2727272727
243 0.1444970182 0.3790044598 0 199 3.2757201646
244 0.0903849614 0.2099036383 0 200 3.2786885246
245 0.7495674478 0.3718116891 0 201 3.2816326531
246 0.3993815067 0.5477964469 0 202 3.2845528455
247 0.3002021254 0.9595262285 0 202 3.2712550607
248 0.1993072331 0.0961488824 0 203 3.2741935484
249 0.7743364166 0.517464056 0 204 3.2771084337
250 0.9217377309 0.3755808023 0 205 3.28
251 0.2226851696 0.5941409057 0 206 3.2828685259
252 0.9971864657 0.0821710745 0 206 3.2698412698
253 0.4349661632 0.147301691 0 207 3.2727272727
254 0.8724651694 0.5251819048 0 207 3.2598425197
255 0.3263723572 0.5263145452 0 208 3.262745098
256 0.1529355222 0.0996218301 0 209 3.265625
257 0.1363225598 0.7239382654 0 210 3.2684824903
258 0.0853727386 0.8505166733 0 211 3.2713178295
259 0.3750641103 0.7982758703 0 212 3.2741312741
260 0.5079757611 0.1710822453 0 213 3.2769230769
261 0.4890405015 0.2734821065 0 214 3.2796934866
262 0.7295855793 0.1969725988 0 215 3.2824427481
263 0.9874681714 0.9041749265 0 215 3.2699619772
264 0.4136242114 0.9627867019 0 215 3.2575757576
265 0.7738113323 0.9087061945 0 215 3.2452830189
266 0.1823072349 0.7653469148 0 216 3.2481203008
267 0.7174593305 0.2717026683 0 217 3.2509363296
268 0.9912234836 0.1062477615 0 218 3.2537313433
269 0.7320112315 0.8411129085 0 218 3.2416356877
270 0.7323810157 0.5570209829 0 219 3.2444444444
271 0.3651869739 0.6937718422 0 220 3.2472324723
272 0.7298979177 0.7872261529 0 220 3.2352941176
273 0.3006578303 0.5028248979 0 221 3.2380952381
274 0.8751765124 0.2267896556 0 222 3.2408759124
275 0.5611905666 0.8834176227 0 222 3.2290909091
276 0.4875087711 0.1023034433 0 223 3.231884058
277 0.5094368116 0.2765539823 0 224 3.2346570397
278 0.5504144281 0.8779626243 0 224 3.2230215827
279 0.5740094728 0.3034233257 0 225 3.2258064516
280 0.9933357625 0.7484869591 0 225 3.2142857143
281 0.7929299628 0.605170502 0 226 3.2170818505
282 0.8497028926 0.4500660073 0 227 3.219858156
283 0.0555876468 0.8121899138 0 228 3.222614841
284 0.4812267422 0.6311058503 0 229 3.2253521127
285 0.6582935839 0.8504138967 0 229 3.2140350877
286 0.3911293662 0.738120908 0 230 3.2167832168
287 0.188694882 0.8661842341 0 231 3.2195121951
288 0.3424062726 0.417229485 0 232 3.2222222222
289 0.2435655882 0.9424346006 0 233 3.2249134948
290 0.4000157732 0.9434505513 0 233 3.2137931034
291 0.0389355932 0.9563752588 0 234 3.2164948454
292 0.5733102912 0.3458460795 0 235 3.2191780822
293 0.1294994294 0.4098463591 0 236 3.2218430034
294 0.926019307 0.6344102548 0 236 3.2108843537
295 0.3814087528 0.8993290022 0 237 3.213559322
296 0.7578068468 0.3231502679 0 238 3.2162162162
297 0.7310414028 0.825623838 0 238 3.2053872054
298 0.6420993438 0.419960305 0 239 3.2080536913
299 0.4793863709 0.3076413534 0 240 3.2107023411
300 0.0037871441 0.0029688338 0 241 3.2133333333
301 0.2448076955 0.5671725325 0 242 3.2159468439
302 0.4661154051 0.2295924093 0 243 3.2185430464
303 0.36930943 0.8857310121 0 244 3.2211221122
304 0.3572417131 0.1984474642 0 245 3.2236842105
305 0.2764015003 0.1939044278 0 246 3.2262295082
306 0.8684314318 0.048981272 0 247 3.2287581699
307 0.1279663827 0.8775310513 0 248 3.2312703583
308 0.8908225355 0.1700461719 0 249 3.2337662338
309 0.398326397 0.1305483467 0 250 3.2362459547
310 0.7908635058 0.6400353607 0 250 3.2258064516
311 0.8955909328 0.3764606796 0 251 3.2282958199
312 0.1071651445 0.5049448893 0 252 3.2307692308
313 0.7565128732 0.763343131 0 252 3.2204472843
314 0.3123345973 0.7020910781 0 253 3.2229299363
315 0.4655419165 0.6145169211 0 254 3.2253968254
316 0.6672522139 0.6372957082 0 255 3.2278481013
317 0.6635651809 0.9819036358 0 255 3.2176656151
318 0.6247878695 0.127244347 0 256 3.2201257862
319 0.5941740547 0.970080546 0 256 3.210031348
320 0.9988885495 0.2502668618 0 256 3.2
321 0.9783022132 0.20185554 0 257 3.2024922118
322 0.3149367479 0.4338266102 0 258 3.2049689441
323 0.3212794511 0.238472563 0 259 3.2074303406
324 0.3447484876 0.2569460579 0 260 3.2098765432
325 0.5774970598 0.8644833954 0 260 3.2
326 0.5122585884 0.5014380336 0 261 3.2024539877
327 0.8016866498 0.7572381712 0 261 3.1926605505
328 0.42842652 0.4733622481 0 262 3.1951219512
329 0.510826629 0.1110499054 0 263 3.1975683891
330 0.4305995296 0.7612070464 0 264 3.2
331 0.4679404555 0.8996453224 0 264 3.1903323263
332 0.6911346091 0.7526858121 0 264 3.1807228916
333 0.4971439272 0.8483858197 0 265 3.1831831832
334 0.7984836257 0.4162813135 0 266 3.1856287425
335 0.2310710754 0.2612851929 0 267 3.1880597015
336 0.8011489461 0.4693746172 0 268 3.1904761905
337 0.3552476531 0.0636488784 0 269 3.1928783383
338 0.7744868653 0.102462046 0 270 3.1952662722
339 0.7977180442 0.9901849809 0 270 3.185840708
340 0.1842386064 0.4683004539 0 271 3.1882352941
341 0.9785840376 0.7304153172 0 271 3.1788856305
342 0.9424641396 0.5138280894 0 271 3.1695906433
343 0.2419072781 0.6984591533 0 272 3.1720116618
344 0.2256153792 0.1638436435 0 273 3.1744186047
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Sheet1

Sheet2

Sheet3