Planification d'un voyage
La vitesse moyenne des voitures voyageant d'Indianapolis, dans l'Indiana, à Chicago, dans l'Illinois, est décrite par une TriangularDistribution.
In[1]:=
![Click for copyable input](assets.fr/travel-planning/In_26.png)
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,
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AlphaIntegration`LinguisticAssistantBoxes["45", 4, Automatic,
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NamespaceBox["LinguisticAssistant",
DynamicModuleBox[{Typeset`query$$ = "82 mph", Typeset`boxes$$ =
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DynamicBox[ToBoxes[
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Out[1]=
![](assets.fr/travel-planning/O_24.png)
La fonction de densité de probabilité pour la loi de la vitesse.
In[2]:=
![Click for copyable input](assets.fr/travel-planning/In_27.png)
Plot[PDF[speed\[ScriptCapitalD], Quantity[x, "mph"]], {x, 50, 85}]
Out[2]=
![](assets.fr/travel-planning/O_25.png)
Calculez la distance entre les villes, en supposant que vous conduisiez.
Afficher l'entrée complète de Wolfram Language
Out[3]=
![](assets.fr/travel-planning/O_26.png)
In[4]:=
![Click for copyable input](assets.fr/travel-planning/In_29.png)
distance =
TravelDistance[{Entity[
"City", {"Indianapolis", "Indiana", "UnitedStates"}],
Entity["City", {"Chicago", "Illinois", "UnitedStates"}]},
TravelMethod -> "Driving"]
Out[4]=
![](assets.fr/travel-planning/O_27.png)
Déterminez la durée prévue du voyage.
In[5]:=
![Click for copyable input](assets.fr/travel-planning/In_30.png)
Expectation[distance/v, v \[Distributed] speed\[ScriptCapitalD]]
Out[5]=
![](assets.fr/travel-planning/O_28.png)
Convertissez en heures et en minutes.
In[6]:=
![Click for copyable input](assets.fr/travel-planning/In_31.png)
Expectation[distance/v, v \[Distributed] speed\[ScriptCapitalD]];
UnitConvert[%, MixedUnit[{"Hours", "Minutes"}]]
Out[6]=
![](assets.fr/travel-planning/O_29.png)
En supposant que le kilométrage en fonction de la vitesse de la voiture est donné par la fonction d'interpolation suivante, la quantité attendue d'essence nécessaire pour le voyage peut être calculée à l'aide de NExpectation.
In[7]:=
![Click for copyable input](assets.fr/travel-planning/In_32.png)
mpg = Interpolation[{Quantity[{40, 50, 60, 70, 80}, "miles per hour"],
Quantity[{33, 32, 28, 25, 20}, "miles per gallon"]} //
Transpose, InterpolationOrder -> 1];
In[8]:=
![Click for copyable input](assets.fr/travel-planning/In_33.png)
NExpectation[distance/mpg[v], v \[Distributed] speed\[ScriptCapitalD]]
Out[8]=
![](assets.fr/travel-planning/O_30.png)