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In particular, E(X2jY = y) is obtained when g(X)=X2 and Var(XjY =y)=E(X2jY =y) ¡E(XjY =y)2 Remark We always suppose that åx jg(x)jfXjY(xjy)•¥ Definition Denote j(y) = E(XjY = y) Then E(XjY) def= j(Y) In words, E(XjY) is a random variable which is a function of Y taking value E(XjY =y) when Y =y The E(g(X)jY) is defined similarly In particular E(X2jY) is obtained when g(X · Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeWhence ym is integral if and only if n = 2k 1 Adding the two equations (3), we get xy = ,q 2, so that Xm is integral if and only if ym is integral
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Variables, eg E(XYZ)=E(X)E(Y)E(Z)) 10 COV(X,Y) = E(X E(X)) * (Y E(Y) = E(XY) E(X)E(Y) Question What is COV(X,X)?A > D B B H O J G A > H J H < V Y² B X E Y = K i b k h d k l j Z g L j _ h \ Z g b y b j _ d h f _ g ^ Z p b b \ h l g h r _ gY Ǘ V X e ̒ ́AAPS/ Y X P W ł BAPS/ Y X P W PlanWizard ́A E v \ E ɓ 琶 Y I _ 쐬 A Y v L ̃X P W O W b N L x ɓ ڂ G W ɂ \ Ȑ Y v ̗ Ă ɍs ܂ B ܂ A ނ̔ v Ă ܂ B
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If/actually had a gradient x* = V/(x) at x in the sense of Gateaux (or Frechet), one would in particular have d/(x) = {V/(x)} (see Moreau 5, p ) It is immediate from (12) that dfix) is a weak* closed convex set in E* for each xGP, and that the effective domain domd/ = {x dfix) ^ 0} of the subgradient mapping 3/ x—>3/(x), ie, the set of points where / is subdifferentiable, isXY (x y) (mean and variance only;1(X)intoG 2(X) Clearly (v 1,v 2) ∈ Im φ, since otherwise G 1(X) would map into X 1 or X 2 Assume that there is an edge e ∈ X such that neither e 1 nor e 2 is in Im φ Let Y be the connected component of X −{e} containing v From the connectedness of G 1(X) it follows that Im φ ⊆ G 2(Y) Now the restriction of φ to G 1(Y) is an
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