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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.

I tried integration by parts but the integral I end up with makes no sense to me.

Sorry, it's a definite integral in from -inf to inf.

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...

Thanks a lot HallsofIvy, t = 1 provided I did the rest of the question right.

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...

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.

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.

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...

got it, thanks.

I end up with k=1, still not sure if I'm right...

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

should I be posting this question in the statistics section of pf?

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)...

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