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This is a slightly modified question from Sheldon Ross 9th ed Assume all RVs are discrete I am asked to prove the following equality $$\mathbb{E}Xg(Y)Y = g(Y)Nov 03, 10 · Let G = (X, Y;G(X) E h(Y) Notes 1 E(XY) = E(X)E(Y) is ONLY generally true if X and Y are INDEPENDENT 2 If X and Y are independent, then E(XY) = E(X)E(Y) However, the converse is not generally true it is possible for E(XY) = E(X)E(Y) even though X and Y are dependent Probability as an Expectation

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80 Example Let X be a discrete random variable with PGF GX(s) = s 5 (2 3s2) Find the distribution of X GX(s) = 2 5 s 3 5 s3 G X(0) = P(X = 0) = 0 G′ X(s) = 2 5 9 5 s2 G′ X(0) = P(X = 1) = 2 5 G′′ X(s) = 18 5 s 1 2 G′′ X(0) = P(X = 2) = 0 G′′′ X(s) = 18 5 1 3!Apr 02, 11 · (this is g^1(g(x)) = x)) perhaps a picture will make more sense x>g(x) = y> z = f(y) = f(g(x)) that is what f o g does so to undo it, we go backwards z>y>x what takes z>y?For any function g, the mean or expected value of g(X) is defined by E(g(X)) = sum g(x k) p(x k) Ex Roll a fair die Let X = number of dots on the side that comes up Calculate E(X2) E(X2) 2= 2sum_{i=1}^{6} i p(i) = 1 p(1) 2 2 p(2) 32 p(3) 42 p(4) 5 p(5) 62 p(6) = 1/6*() = 91/6 E(X) is the expected value or 1st moment

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And hence jˆ E(x) ˆ E(y)j d(x;y) Chapter 4, problem 21 Suppose Kand F are disjoint sets in a metric space X, Kis compact, Fis closed Prove that there exists >0 such that d(p;q) > if p2K;q2F Show that the clonclusion may fail for two disjoint closed sets if neither is compact SolutionTh ey are system s o rien tedT h ey've d isco veredEE(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 equivalent statements 3

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Here h(x,y)is a 2dimoensional guassian function can any you help me in getting the code for matlab ?Aug 30, 12 · I was wondering whether g(EX,EY) or Eg(X,Y) would bring me closer to the actual value z?Conditioning on the discrete level Example A fair coin is tossed 10 times;

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0 Comments Show Hide 1 older comments Sign in to comment Sign in to answer this questionFeb 01, 14 · what does the expression meansbasically what does the expression g(x,y) means ?E(XY) = E(X)E(Y) More generally, Eg(X)h(Y) = Eg(X)Eh(Y) holds for any function g and h That is, the independence of two random variables implies that both the covariance and correlation are zero But, the converse is not true Interestingly, it turns out that this result helps us prove

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3 the vicinal preorder is linear on X (equivalently on Y);See all Words by Length at More Words Find that difficult long word here!E(var(yx)) = e(e(y2x)) e(e(yx)2) We have already seen that the expected value of the conditional expectation of a random variable is the expected value of the original random variable, so applying this to Y 2

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That is f^1 what takes y>x that is g^1 do f^1 first, and then g^1, is g^1(f^1(z)) = g^1 o f^1(z) since this undoes what f o g does, it must beI think that if you manage to state your question precisely, the answer will be E( g(X,Y)), but you haven't defined the meaning of "best" in your original post and to say a random result is "closer" to something has no specific meaningHomework 6 Solutions Math 171, Spring 10 Henry Adams 386 Let fbe a continuous function from R to R Prove that fx f(x) = 0gis a closed subset of R

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I' = ¥yy f y x i 2x y ④May 31, 07 · g(x) would mean that the function is called "g" Most of the time, the first time you are introduced to this notation, "f" is used because it is the letter that starts the word "function" and this helps you make the connection You can use any symbol for your function name, f(x), g(x), h(y), q(z) and yourmomma(x) are all legal function namesI have said this consistently The stimulus depressed America U/e rose and deflation took hold Then when it was wound back there was less capacity to handle the demand So it basically destroyed capital formation and reset the economy at a lower natural

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The Substitution Rule If u = g(x) is a differentiable function whose range is an interval I and f is continuous on I, then Z f(g(x))g0(x)dx = f(u)du Example Calculate R tanx dx Solution Z tanx dx = sinx cosx dx This suggests substitution u = cosx, since then du = −sinx dx and so, sinx dx = −du ZG′′′ X(0) = P(X = 3) = 3 5 G(r) X (s) = 0 ∀r ≥ 4 1Hw7pdf Mame Phan Vu 15 5 ③ and D A B C ⑥ zero negative positive g(x y = xx y ¥ Hi¥÷y = Ey or t r"Y;7ti o Sai;

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606 A BR0NDSTED AND R T ROCKAFELLAR August functions determined by its subgradients, ie (B) f(y) = sup{/(x) (yx, x*) xEdomdf, x* G df(x)} for all y G Eσ= E(εT ε)o a o = E(ε εb – ε) = Eu(,x – yβ,x – ε)o ∴ F = σdA F = Eu(,x – yβ,x – ε)o dA F = u,x EA d β,x yE A d εoEAd M = yσdA M = yE u(,x – yβ,x – ε)o dA M = u,x yE A β,x y d 2 EA d yε d oEA X$ yE A d = 0 % F = u,x EA d εoEAd M = β,x y d yεoEA 2 EA dE(y) Similarly one can show ˆ E(y) d(x;y) ˆ E(x);

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Example 5 X and Y are jointly continuous with joint pdf f(x,y) = (e−(xy) if 0 ≤ x, 0 ≤ y 0, otherwise Let Z = X/Y Find the pdf of Z The first thing we do is draw a picture of the support set (which in this case is the firstY = C I G (XM) National income with government interference From the national income, some will be used for consumption, saving, and other's used for paying taxes With adding of variable taxes on national income, then the formula is Y = C S T To see the balance of national income with the adding of government spending and taxDiscutir a quantidade de soluções reais de uma equação `g(x) = f(x)` pode ser facilitada pela exibição no mesmo plano cartesiano dos gráficos de `g(x)` e `f(x)` Dispensando o uso de calculadoras e/ou programas CAM (computer aided mathematics) um bom esboço dos gráficos de f e g vai ajudar a análise da equação que as envolve

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By g x where a and b are constants, and g x is a differentiable function of x In chapter 64, we saw that a first order equation has a oneparameter family of solutions, and that the specification of an initial condition y x0 y0 uniquely determines a solution In the case of second order equations, the basic theorem is thisX or y, eg is a crossword puzzle clue Clue x or y, eg x or y, eg is a crossword puzzle clue that we have spotted 6 times There are related clues (shown below)The random variable X is the number of heads in these 10 tosses, and Y — the number of heads in the first 3 tosses In spite of the fact that Y emerges before X it may happen that

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