文档介绍：Example
A student attempts a multiple choice exam (options A to F for each question), but having done no work, selects his answers to each question by rolling a fair die (A = 1, B = 2, etc.).
If the exam contains 100 questions, what is the probability of obtaining a mark below 20?
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Simulation
Now, let us simulate a large number of realisations of students using this random method of answering multiple choice questions. We still require the same Binomial distribution with n=100 and a=
This can be done on R using mand rbinom.
For example, let’s simulate 1000 students.
> xsim=rbinom(1000,100,1/6)
> xsim
[1] 18 22 9 17 18 20 21 16 8 18 11 16 16 13 16 14 25 15 16 17
[21] 13 25 11 24 17 16 13 21 10 17 18 10 17 18 19 17 19 15 13 12
[41] 15 11 21 23 19 14 19 25 23 19 20 17 17 15 16 14 13 16 17 14
[61] 24 21 19 8 18 20 22 16 15 20 19 17 13 15 13 21 22 12 12 12
[81] 11 14 11 12 16 16 17 21 17 16 17 14 9 17 16 17 12 20 16 17
[101] 18 13 15 16 12 15 17 16 17 26 18 14 21 15 10 23 12 16 16 12
[121] 17 18 22 17 18 14 19 22 13 17 21 15 21 16 17 16 16 28 16 17
[141] 18 19 16 11 14 18 16 18 18 14 20 13 19 19 22 22 13 17 19 17
[161] 18 20 11 22 19 25 15 15 17 18 5 15 14 13 18 15 17 15 20 17
[181] 16 14 23 17 16 10 12 16 21 30 16 13 22 14 15 16 17 14 16 18
[201] 14 20 16 19 25 14 15 24 22 19 15 17 22 10 20 13 10 15 14 22
[221] 17 12 16 19 20 17 15 21 14 13 21 11 19 9 21 22 16 13 13 12
[241] 14 13 18 8 14 18 10 16 10 12 21 18 15 17 16 8 19 17 11 18
[261] 23 17 20 16 12 20 11 16 22 17 16 13 22 20 15 15 20 17 22 14
[281] 18 23 18 20 20 16 19 16 15 19 18 17 14 22 15 24 17 15 17 22
[301] 18 22 10 19 24 21 16 14 11 14 20 15 21 11 17 16 20 19 13 14
[321] 17 17 19 15 17 13 18 23 16 12 25 13 13 21 19 16 20 27 19 18
[341] 18 24 15 23 13 13 14 15 23 13 19 15 11 19 17 12 15 15 17 14
[361] 18 20 17 13 16 14 13 20 18 15 18 16 17 20 14 19 21 12 13 17
[381] 22 17 19 16 14 18 16 18 12 16 13 15 16 9 15 16 18 22 14 16
[401] 14 17 12 16 21 16 21 13 14 19 18 18 16 19 17