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8: Probability and Statistics Solvers and Properties
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Core Algorithms
Compute Conditional Probabilities and Expectations
Compute the probabilities and expectations under prescribed conditions in arbitrary distributions.
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conditionalprobabilitiesandexpectations = {HoldForm[ Probability[x < 2 \[Conditioned] 1/2 < x^2 < 5, x \[Distributed] NormalDistribution[0, 1]]], HoldForm[ Probability[ x + y < 7/10 \[Conditioned] y > 1/3, {x, y} \[Distributed] DirichletDistribution[{1, 3, 4}]]], HoldForm[ NProbability[x^2 + 11 x > 32 Pi \[Conditioned] x > 3, x \[Distributed] PoissonDistribution[2]]], HoldForm[ Expectation[x + 2 \[Conditioned] 2 < x < 15, x \[Distributed] ExponentialDistribution[3]]], HoldForm[ Expectation[ x + y + 5 \[Conditioned] z > 2, {x, y, z} \[Distributed] MultinomialDistribution[5, {p, q, r}]]], HoldForm[ NExpectation[x^2 + 1 \[Conditioned] x > 1/3, x \[Distributed] LaplaceDistribution[0, 3]]]};
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FormulaGallery[forms_List] := Module[{vals = ParallelMap[ReleaseHold, forms]}, TraditionalForm@ Grid[Table[{forms[[i]], vals[[i]]}, {i, Length[forms]}], Dividers > All, Spacings > {1, 2}, Alignment > {Center, Center}, BaseStyle > {FontFamily > "Verdana"}, Background > {None, {{Hue[.6, .15, .9], GrayLevel[.9]}}}, FrameStyle > Directive[Thick, White]]]
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Pane[FormulaGallery[conditionalprobabilitiesandexpectations] , 550]
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