[問題] 迴圈加速

[Serenede (Serenede)]

sav = 0; iter = 10000000;

For[i = 1, i <= iter, i++,
  If[Random[]^2 < 1/2, sav = sav + 1;]
  ] // Timing

2 sav/iter // N

這樣居然也算了23秒，覺得有點太久，請問要怎樣寫才會快呢?

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※ 編輯: Serenede (114.26.112.191), 12/21/2014 00:39:59
→ biglion: Nest[UnitStep[(1/2-Random[]^2)]+#&,0,10000000]
推 sunev: RandomVariate[NormalDistribution[1/Sqrt[2], 1/Sqrt[12]/
→ sunev: /Sqrt[10000000]]]
推 chungyuandye: AbsoluteTiming@Total@NestList[If[Random[]^2<0.5,
→ chungyuandye: 1,0]&,0,iter]