핵심 알고리즘

수식에 대한 기대값 연산

식의 기대값을 모수, 비모수, 미분, 공식화된 분포로 연산합니다.

In[1]:=

expectations = {HoldForm[

Expectation[E^(2 x),

x \[Distributed] PoissonDistribution[\[Lambda]]]],

HoldForm[

Expectation[(x - 1)^2 + Abs[x] - 3 x,

x \[Distributed] NormalDistribution[0, 1]]],

HoldForm[

Expectation[

x^10 + 11, {x, y} \[Distributed]

MultivariatePoissonDistribution[1, {2, 3}]]],

HoldForm[

Expectation[

x + y^2 + UnitBox[z - 2/3], {x, y, z} \[Distributed]

DirichletDistribution[{2, 3, 4, 7}]]],

HoldForm[

Expectation[x^2 + x + 54,

x \[Distributed]

CensoredDistribution[{3, 11},

ExponentialDistribution[\[Lambda]]]]],

HoldForm[

Expectation[x^5 + 3 x + 166,

x \[Distributed]

EmpiricalDistribution[{1, 2, 4 E, 5, 7 Pi, 9}]]],

HoldForm[

Expectation[E^x + 2,

x \[Distributed]

ProbabilityDistribution[3/4 (x^2 + 2 x), {x, 0, 1}]]],

HoldForm[

NExpectation[

x^2 + E^(E^(-y^2)) + 1, {x, y} \[Distributed]

BinormalDistribution[1/2]]]};

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