含有数量的截断分布
美国红莓的直径服从均值为 16 毫米、标准差为 1.6 毫米的正态分布. 果实的直径必须大于 15 毫米才能作为单品出售;否则用来生产红莓酱. 求作为单品出售的果实的尺寸分布.
In[1]:=

cran\[ScriptCapitalD] =
NormalDistribution[Quantity[16, "Millimeters"],
Quantity[1.6, "Millimeters"]];
\[ScriptCapitalD] =
TruncatedDistribution[{Quantity[15, "Millimeters"], \[Infinity]},
cran\[ScriptCapitalD]];
比较概率密度函数.
In[2]:=

Plot[{PDF[cran\[ScriptCapitalD], Quantity[x, "Milimeters"]],
PDF[\[ScriptCapitalD], Quantity[x, "Milimeters"]]}, {x, 10, 22},
PlotLegends -> {"cran\[ScriptCapitalD]", "\[ScriptCapitalD]"},
Filling -> Axis, AxesLabel -> {"mm"}]
Out[2]=

假设一磅包装的红莓的体积大约为 30 in3,求其中红莓数量的平均下限和上限.
In[3]:=

lowerbound =
Floor[NExpectation[
Divide[Quantity[30, "Inches"^3],
Volume[Cuboid[{0, 0, 0}, {x, x, x}]]],
x \[Distributed] \[ScriptCapitalD]]]
Out[3]=

In[4]:=

upperbound =
Ceiling[NExpectation[
Divide[Quantity[30, "Inches"^3], Volume[Ball[{0, 0, 0}, x/2]]],
x \[Distributed] \[ScriptCapitalD]]]
Out[4]=
