Page 746Page 1USING EXCELS RAND() FUNCTION0.5110 0.9236 0.3844 0.2836 - =RAND()0.4221 0.3155 0.9605 0.13420.4178 0.3363 0.6546 0.75710.9421 0.7891 0.9254 0.76150.4636 0.1189 0.3828 0.23330.6932 0.7949 0.1763 0.05580.5107 0.0541 0.2805 0.42730.0998 0.4242 0.3612 0.06950.8872 0.8829 0.2115 0.6684Each cell contains thefunction Rand(). Each time youupdate the spreadsheet or press F9 the block of cells willproduce a new set of randomnumbers.A B C D E123456789101112使用EXCEL的RAND()函数0.6101 0.9634 0.0629 0.7579 - =RAND()0.2024 0.9171 0.2324 0.20600.3983 0.5702 0.1150 0.00670.5401 0.4798 0.3324 0.72890.3553 0.6390 0.0339 0.93330.3633 0.0883 0.3636 0.09220.8209 0.9104 0.4767 0.74080.3269 0.4945 0.4727 0.62610.4728 0.1746 0.9502 0.8678每个单元格都含有函数Rand()。每次更新工作表或按F9，这些单元格会生成新的一系列的随机数。USING VBAS RND FUNCTION TOPRODUCE A LIST OF RANDOMNUMBERSList0.045350.414030.862620.790480.373540.961950.871450.056240.949560.36402A B C D E123456789101112使用 VBA的RND 函数来生成一列随机数列表0.045350.414030.862620.790480.373540.961950.871450.056240.949560.36402UN-18BUSING EXCELS FREQUENCY FUNCTIONTO TEST THE DISTRIBUTION OF RAND()Randomnumbers Bin Frequency0.6110 - =RAND() 0.1 10.4489 0.2 10.8323 0.3 00.7128 0.4 10.7330 0.5 2 - =FREQUENCY(A3:A12,D3:D12)0.9557 0.6 00.0647 0.7 10.1735 0.8 20.4988 0.9 10.3742 1 1Each cell in the range A3:A12 contains the formula Rand(). Pressing F9 will produce a new set ofrandom numbers and frequencies.A B C D E F1234567891011121314使用EXCEL的FREQUENCY函数检验RAND()的分布随机数 分组 频数0.1401 - =RAND() 0.1 30.7916 0.2 20.2833 0.3 20.0665 0.4 00.4850 0.5 2 - =FREQUENCY(A3:A12,D3:D12)0.0392 0.6 00.0212 0.7 00.2624 0.8 10.4814 0.9 00.1147 1 0在区域A3:A12中的每个单元格都含有函数Rand()。每次按F9会生成新的一系列的随机数和频数。Uniformly Distributed Random NumbersRuns 1,000,000Starttime 17:37:03Bin Output Stoptime 17:37:041 100,070 Elapsed 0:00:012 100,6593 99,6524 99,7655 100,0016 99,8327 99,8128 99,8549 100,23410 100,121Graph titleFrequency Distribution of 1,000,000 runs of VBAs Rnd functionF r e q u e n c y D is tr ib u tio n o f 1 ,0 0 0 ,0 0 0 r u n s o f V B A s R n d fu n c tio n1 2 3 4 5 6 7 8 9 1 09 9 , 0 0 09 9 , 2 0 09 9 , 4 0 09 9 , 6 0 09 9 , 8 0 01 0 0 , 0 0 01 0 0 , 2 0 01 0 0 , 4 0 01 0 0 , 6 0 01 0 0 , 8 0 0Frequency Distribution of 1,000,000 runs of VBAs Rnd functionF r e q u e n c y D is tr ib u tio n o f 1 ,0 0 0 ,0 0 0 r u n s o f V B A s R n d fu n c tio n1 2 3 4 5 6 7 8 9 1 09 9 , 0 0 09 9 , 2 0 09 9 , 4 0 09 9 , 6 0 09 9 , 8 0 01 0 0 , 0 0 01 0 0 , 2 0 01 0 0 , 4 0 01 0 0 , 6 0 01 0 0 , 8 0 0均匀分布的随机数运行 1,000,000开始时间 17:37:03分组 输出 停止时间 17:37:041 100,070 用时 0:00:012 100,6593 99,6524 99,7655 100,0016 99,8327 99,8128 99,8549 100,23410 100,121图表标题运行1,000,000次的VBA的Rnd函数的频数分布运 行 1 ,0 0 0 ,0 0 0 次 的 V B A 的 R n d 函 数 的 频 数 分 布1 2 3 4 5 6 7 8 9 1 09 9 , 0 0 09 9 , 2 0 09 9 , 4 0 09 9 , 6 0 09 9 , 8 0 01 0 0 , 0 0 01 0 0 , 2 0 01 0 0 , 4 0 01 0 0 , 6 0 01 0 0 , 8 0 0运 行 1 ,0 0 0 ,0 0 0 次 的 V B A 的 R n d 函 数 的 频 数 分 布1 2 3 4 5 6 7 8 9 1 09 9 , 0 0 09 9 , 2 0 09 9 , 4 0 09 9 , 6 0 09 9 , 8 0 01 0 0 , 0 0 01 0 0 , 2 0 01 0 0 , 4 0 01 0 0 , 6 0 01 0 0 , 8 0 0PRODUCING LISTS OF RANDOMNUMBERSSeed 334Output:Each rundifferentOutput:Each runsame0.36654 0.297080.85005 0.706530.54326 0.654630.21992 0.968480.35859 0.489990.12416 0.723730.22022 0.065180.94125 0.600340.18800 0.253820.90571 0.70398Note: to see the effect of the Run Random_Samebutton, erase the cells B5:B14. Changing the seed in cellB2 changes the output in column B.A B C12345678910111213141516生成随机数列种子 334输出:每次不同输出:每次相同0.36654 0.297080.85005 0.706530.54326 0.654630.21992 0.968480.35859 0.489990.12416 0.723730.22022 0.065180.94125 0.600340.18800 0.253820.90571 0.70398注:若要观察“RunRandom_Same”按钮的效果，清空B5:B14。改变B2中的种子可改变B列中的输出。-0.889391.087806 Bin Frequency-1.88485 -3 30.58754 -2.9 0-0.71044 -2.8 11.107367 -2.7 0-1.41278 -2.6 20.723298 -2.5 2-0.24339 -2.4 41.148851 -2.3 2-0.35236 -2.2 40.047868 -2.1 80.613745 -2 71.476174 -1.9 60.511462 -1.8 6-0.80273 -1.7 9-2.2763 -1.6 110.585451 -1.5 13-0.50902 -1.4 190.77227 -1.3 16-1.46378 -1.2 21-0.3842 -1.1 170.391296 -1 14-1.81106 -0.9 22-0.21809 -0.8 29-2.05333 -0.7 260.008682 -0.6 28-1.56173 -0.5 29-1.11175 -0.4 421.342078 -0.3 40-0.21253 -0.2 40-0.28522 -0.1 350.017558 0 42-1.75057 0.1 50-0.57748 0.2 412.526031 0.3 49-0.98518 0.4 38-0.28865 0.5 27-1.2998 0.6 440.288329 0.7 29-0.73598 0.8 29-1.70106 0.9 180.262426 1 22-0.1658 1.1 27-0.26116 1.2 160.553334 1.3 151.864892 1.4 140.501375 1.5 19-0.69468 1.6 10-0.62682 1.7 13-1.03044 1.8 8-0.86478 1.9 60.855259 2 10.677157 2.1 8-1.20893 2.2 43210- 1- 2- 301 02 03 04 05 06 0-0.51077 2.3 10.592639 2.4 20.002027 2.5 50.088739 2.6 1-0.17279 2.7 11.563808 2.8 00.607752 2.9 0-0.8817 3 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