Recent content by erica1451

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    Random Walk Question: Expected Value, Variance & Lim n→∞

    Homework Statement Let (X1, X2, ..., Xn,...) be iid increments (with mean µ and variance ∂^2) of a random walk Sn=X1+X2+...+Xn. What are the expected value, variance of Sn? Prove that lim n-> ∞ Sn =+ ∞ if µ>0 and lim n-> ∞ Sn =- ∞ if µ<0 Homework Equations The Attempt at a...
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    Question about Independent Normal Variables

    Homework Statement Let X,Y be two independent normal N(0,1) and N(0,2) variables, and Z=XY. Suppose that E(X^4)=3 a) Compute Var(X), Var(Y), Var(Z), Cov(X,Y), Cov(Y,Z), Var(X+Y), Var(X+Z) b) By computing E[(X^2)(Z^2)], prove that X,Z are not independent.Homework Equations Var(X)=E(X^2)-E(X)^2...
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    Understanding Critical Points in Multivariable Functions

    Thank you!
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    Understanding Critical Points in Multivariable Functions

    Can anyone help?
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    Understanding Critical Points in Multivariable Functions

    Homework Statement f(x,y,z)=(xy+yz+xz)/(1+x^2+y^2+z^2) Explain why f has no absolute maximum or minimum. How about critical points? Homework Equations Hint: it is simplest to make 3 cases: a) x+y+z does not =0 b) x+y+z=0 c) x=y=z=0 The Attempt at a Solution I did cases b and c...
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    Prove Laplace Operator Unchanged in 3D Rotation

    I understand how to do the problem now. Thanks for your help.
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    Prove Laplace Operator Unchanged in 3D Rotation

    Homework Statement Prove that the Laplacian operator in dimension 3 is unchanged if the coordinates are rotated. Homework Equations If S is a rotation (S*S=I) and if x'=Sx then show d^2/dx1'^2 + d^2/dx2'^2 +d^2/dx3'^2 = d^2/dx1^2 + d^2/dx2^2 + d^2/dx3^2 The Attempt at a Solution I...
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