WOLFRAM

Wolfram 语言与系统参考资料中心

分析一场网球赛

在一场双人比赛中， 假设发球得分的概率是 . 可视化 ，17分支的随机游走图表.

Wolfram Language code: proc = With[{p = 3 / 5, q = 2 / 5}, DiscreteMarkovProcess[17, (⁠| | | | | | | | | | | | | | | | | | | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | p | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | p | 0 | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | q | p | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | p | 0 | 0 | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | q | 0 | 0 | p | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | p | 0 | 0 | 0 | 0 | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | q | 0 | 0 | p | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | p | 0 | 0 | 0 | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | q | 0 | 0 | 0 | 0 | p | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | p | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | p | q | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | p | q | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | p | q | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | p | q | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | p | q | 0 |⁠)]];
Wolfram Language code: Graph[proc, VertexSize -> {"Scaled", 0.07}, VertexLabels -> Thread[Range[17] -> Map[Placed[Style[#, {Bold}], Center]&, states = {"比赛A", "比赛B", "平局", "AdvA", "AdvB", "40-15", "15-40", "40-0", "30-15", "15-30", "0-40", "30-0", "15-15", "0-30", "15-0", "0-15", "0-0"}]], ImageSize -> Large, ImagePadding -> 25]
求 时发球得分的概率：
Wolfram Language code: PDF[proc[∞], 1]//N
求平均吸收时间，即比赛分数：
Wolfram Language code: N[Mean[FirstPassageTimeDistribution[proc, {1, 2}]]]
求访问分支的平均数：
Wolfram Language code: MarkovProcessProperties[proc, "TransientTotalVisitMean"]//N
求分数平局的平均次数：
Wolfram Language code: MarkovProcessProperties[proc, "TransientVisitMean"][[1]]//N