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N C X y b N ͐ X ŃR s ^ @ ̔ A \ t g E G A J A V X e T g s Ă Ђł B ̔ Ǘ V X e E ڋq Ǘ V X e E ^ ƊǗ V X e E T Ǘ V X e E ۋ Ǘ V X e 舵 Ă ܂ BBut then E(XjY =y)=åx xfXjY(xjy)=åx xfX(x)=E(X) 2 2 EE(g(X)jY)=E(g(X)) Proof Set Z = g(X) Statement (i) of Theorem 1 applies to any two rv's Hence, applying it to Z and Y we obtain EE(ZjY)= E(Z) which is the same as EE(g(X)jY)= E(g(X)) 2 This property may seem to be more general statement than (i) in Theorem 1 The proof above shows that in fact these are equivalentI ȃV X e J ɂ A S E m E ȃ\ V 񋟂 Ă ܂ t @ E F A ̕ ɉ Ă A ͂ v t @ N ^ ́A R p N g E E ėp E ێ琫 ܂ B ̖ j Y ɂ A ̃V X e \ z ܂ B ł ɖ Z p ͐ ł́A ̖ ͉ ܂ B

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Exponentialfunktionen haben in den Naturwissenschaften, z B bei der mathematischen Beschreibung von Wachstumsvorgängen, eine herausragende Bedeutung (siehe exponentielles Wachstum ) Als natürliche Exponentialfunktion oder eFunktion bezeichnet man die Exponentialfunktion x ↦ e x {\displaystyle x\mapsto e^ {x}} mit der eulerschen Zahl eF b g A Ĕ p ܂߂ēO r B w ̑؍ݐ ̈ړ ɂ Ă܂ŏڂ ē Ă ܂ B̂ ߁A j łȂ A Ƌ Ɏ ꂽ ʂ ₤ Ƃɂ āA l X ȏǏ P 邱 Ƃ o ܂ B z o X Ɛ A ^ ʂ̋ A ̌^ ǂ A ̎ ̉ P A ~ ̏㏸ A a ̉ P ȂǗl X Ȍ ʂ ҂ł ܂ B 100 3,580 ~

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