Mathematica 教學：隨機樣本

dist={{1,0.4},{4,0.1},{5,0.3},{8,0.03},{9,0.11},{10,0.06}};
ans[data_List]:={RandomChoice[data[[All,2]]->data[[All,1]]],
Plus@@Times@@@data}
ans[dist]

(* 產生樣本數為n的隨機樣本 *)

sample[n_]:=RandomChoice[dist[[All,2]]->dist[[All,1]]]&/@Range[n];

(* 輸出條型圖 *)

mychart[n_]:=Block[{temp},
temp=SortBy[Tally@sample[n],First];
BarChart[temp[[All,2]],
ChartLabels->temp[[All,1]],
LabelingFunction->(Placed[NumberForm[N[#/n],{4,3}],Above]&)]
];

mychart[100000]

(* 中央極限定理，每次抽n個樣本，重覆實驗m次 *)

sim[n_,m_]:=N@Mean[sample[n]]&/@Range[m]
GraphicsGrid@Partition[Histogram[sim[#,100],
PlotRange->{{2,6},Automatic},
AxesOrigin->{0,0}]&/@{10,100,500,1000},2]

Tags: Mathematica 教學, Teaching

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