Recent content by alias

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    Integration of a pdf, expected value

    I integrated the Gaussian distribution, it took a long time but I finally got the right answer. After making a substitution, integration by parts worked. I would like to know if the formula: E[(Y-mu)^4]/[E(Y-mu)^2]^2, is useless for answering this question though. Thanks guys.
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    Integration of a pdf, expected value

    I tried integration by parts but the integral I end up with makes no sense to me.
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    Integration of a pdf, expected value

    Sorry, it's a definite integral in from -inf to inf.
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    Integration of a pdf, expected value

    Homework Statement Show that E[Y^4] = 3, where Y~N(0,1) Homework Equations E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3 E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2) The Attempt at a Solution I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's...
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    Find the curvature at a point(vector function)

    Thanks a lot HallsofIvy, t = 1 provided I did the rest of the question right.
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    Find the curvature at a point(vector function)

    Homework Statement Find the curvature of r(t)= <t^2, lnt, t lnt> at the point P(1,0,0) Homework Equations K(t) = |r'(t) x r''(t)|/(|r'(t)|^3) The Attempt at a Solution r'(t) = <2t, t^-1, lnt+1> r''(t) = <2, -t^-2, t^-1> |r'(t) x r''(t)| = sqrt[t^-4(4 + 4 lnt + ln^2t) + (4...
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    4th moment, show that E[X-mu]^4 is equal to

    I know that the one equation will cover both the discrete and continuous cases, but the question specifically asks to show each case individually and I'm not sure what the specific summation and integral that I have to work out is.
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    4th moment, show that E[X-mu]^4 is equal to

    I got the expansion, thanks. I'm not sure why I need to split the cases for continuous/discrete either. It's asked in the question and I don't know how to prove with continuous/discrete separately.
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    4th moment, show that E[X-mu]^4 is equal to

    Homework Statement X is a random variable with moments, E[X], E[X^2], E[X^3], and so forth. Prove this is true for i) X is discrete, ii) X is continuous Homework Equations E[X-mu]^4 = E(X^4) - 4[E(X)][E(X^3)] + 6[E(X)]^2[E(X^2)] - 3[E(X)]^4 where mu=E(X) The Attempt at a Solution...
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    Find the constant that makes f(x,y) a PDF

    got it, thanks.
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    Find the constant that makes f(x,y) a PDF

    I end up with k=1, still not sure if I'm right...
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    Find the constant that makes f(x,y) a PDF

    The integral of a joint PDF = 1: f(x,y) dxdy = 1 Sorry I don't have a better response.
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    Find the constant that makes f(x,y) a PDF

    should I be posting this question in the statistics section of pf?
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    Find the constant that makes f(x,y) a PDF

    Homework Statement Find the value of k that makes this a probability density function. The question does not specify whether X and Y are independent or dependent. That is actually another part this question. Homework Equations Let X and Y have a joint density function given by f(x,y)...
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    Describe the region of R^3, sphere with inequality

    Thanks a lot for your help. You have a lot of patience!