Wolfram Language

Grandeurs en probabilité et en statistique

Plan de Voyage

La vitesse moyenne des voitures voyageant d'Indianapolis, Indiana, à Chicago, Illinois, est décrite par une TriangularDistribution.

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speed\[ScriptCapitalD] = TriangularDistribution[{\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$$ = "55 mi/h", Typeset`boxes$$ = TemplateBox[{"55", RowBox[{"\"mi\"", " ", "\"/\"", " ", "\"h\""}], "miles per hour", FractionBox["\"Miles\"", "\"Hours\""]}, "Quantity", SyntaxForm -> Mod], Typeset`allassumptions$$ = {}, Typeset`assumptions$$ = {}, Typeset`open$$ = {1, 2}, Typeset`querystate$$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 3.9373779`8.046752092819743, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["45", 4, Automatic, Dynamic[Typeset`query$$], Dynamic[Typeset`boxes$$], Dynamic[Typeset`allassumptions$$], Dynamic[Typeset`assumptions$$], Dynamic[Typeset`open$$], Dynamic[Typeset`querystate$$]], StandardForm], ImageSizeCache->{94., {8., 16.}}, TrackedSymbols:>{ Typeset`query$$, Typeset`boxes$$, Typeset`allassumptions$$, Typeset`assumptions$$, Typeset`open$$, Typeset`querystate$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$$ = "82 mph", Typeset`boxes$$ = TemplateBox[{"82", RowBox[{"\"mi\"", " ", "\"/\"", " ", "\"h\""}], "miles per hour", FractionBox["\"Miles\"", "\"Hours\""]}, "Quantity", SyntaxForm -> Mod], Typeset`allassumptions$$ = {}, Typeset`assumptions$$ = {}, Typeset`open$$ = {1, 2}, Typeset`querystate$$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.2656176`6.875801841788495, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$$], Dynamic[Typeset`boxes$$], Dynamic[Typeset`allassumptions$$], Dynamic[Typeset`assumptions$$], Dynamic[Typeset`open$$], Dynamic[Typeset`querystate$$]], StandardForm], ImageSizeCache->{94., {8., 16.}}, TrackedSymbols:>{ Typeset`query$$, Typeset`boxes$$, Typeset`allassumptions$$, Typeset`assumptions$$, Typeset`open$$, Typeset`querystate$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)}, \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{Typeset`query$$ = "72 mph", Typeset`boxes$$ = TemplateBox[{"72", RowBox[{"\"mi\"", " ", "\"/\"", " ", "\"h\""}], "miles per hour", FractionBox["\"Miles\"", "\"Hours\""]}, "Quantity", SyntaxForm -> Mod], Typeset`allassumptions$$ = {}, Typeset`assumptions$$ = {}, Typeset`open$$ = {1, 2}, Typeset`querystate$$ = { "Online" -> True, "Allowed" -> True, "mparse.jsp" -> 0.250013`6.8495075848939235, "Messages" -> {}}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 4, Automatic, Dynamic[Typeset`query$$], Dynamic[Typeset`boxes$$], Dynamic[Typeset`allassumptions$$], Dynamic[Typeset`assumptions$$], Dynamic[Typeset`open$$], Dynamic[Typeset`querystate$$]], StandardForm], ImageSizeCache->{94., {8., 16.}}, TrackedSymbols:>{ Typeset`query$$, Typeset`boxes$$, Typeset`allassumptions$$, Typeset`assumptions$$, Typeset`open$$, Typeset`querystate$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{Typeset`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)]
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La fonction de densité de probabilité pour la distribution de la vitesse.

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Plot[PDF[speed\[ScriptCapitalD], Quantity[x, "mph"]], {x, 50, 85}]
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Calculez la distance entre les villes, en supposant que vous conduisiez.

Montrer l'entrée complète de Wolfram Language
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GeoGraphics[ Style[Line[ TravelDirections[{Entity[ "City", {"Indianapolis", "Indiana", "UnitedStates"}], Entity["City", {"Chicago", "Illinois", "UnitedStates"}]}]], Thick, Red], GeoBackground -> GeoStyling["StreetMap"], GeoRange -> Quantity[100, "Miles"]]
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distance = TravelDistance[{Entity[ "City", {"Indianapolis", "Indiana", "UnitedStates"}], Entity["City", {"Chicago", "Illinois", "UnitedStates"}]}, TravelMethod -> "Driving"]
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Trouvez le temps prévu de voyage prévu.

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Expectation[distance/v, v \[Distributed] speed\[ScriptCapitalD]]
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Convertissez en heures et minutes.

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Expectation[distance/v, v \[Distributed] speed\[ScriptCapitalD]]; UnitConvert[%, MixedUnit[{"Hours", "Minutes"}]]
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En supposant que la consommation d'essence en fonction de la vitesse de la voiture est donnée par la fonction d'interpolation suivante, la quantité prévue de gaz nécessaire pour le voyage peut être calculée à l'aide de NExpectation.

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mpg = Interpolation[{Quantity[{40, 50, 60, 70, 80}, "miles per hour"], Quantity[{33, 32, 28, 25, 20}, "miles per gallon"]} // Transpose, InterpolationOrder -> 1];
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NExpectation[distance/mpg[v], v \[Distributed] speed\[ScriptCapitalD]]
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