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(*deployswithcanonicalname*)​​
CompoundExpression[
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​​deploy
Sat 14 Oct 2023 20:58:15
- Distribution of intersection of n-sphere and hyperplane projected onto c stats.SE question​
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Clear["Global`*"]
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b=0.5;​​pos[theta_]:={b,Cos[theta]Sqrt[1-b^2],Sin[theta]Sqrt[1-b^2]}​​sphere1=ParametricPlot3D[pos[theta],{theta,0,2Pi},PlotRange->{{-1.5,1.5},{-1.5,1.5},{-1.5,1.5}}];​​sphere2=Graphics3D[{Opacity[.2],Sphere[]}];​​​​Show[sphere1,sphere2,PlotLabel->"Valid x"]​​​​c=Normalize[{1,1,1}];​​Plot[c.pos[theta],{theta,0,2Pi},PlotLabel->"value of <c,x>"]​​cmin=First@Minimize[c.pos[theta],theta];​​cmax=First@Maximize[c.pos[theta],theta];​​vals=Table[c.pos[theta],{theta,0,2Pi,.0001}];​​Histogram[vals,{cmin,cmax,.01},"Probability",AxesOrigin->{0,0}]
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