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    Conditional expectation

    Question 1) I have X and Y independent stoch. variables What is E[X^2 * Y | X] ? does it generally hold that if X and Y are independent, then every function of X (eg X^2) is independent of Y? Does E[X^2 * Y | X] then become E[X^2|X]*E[Y|X] = E[X^2|X]*E[Y] since X^2 is independent of...
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    Multiple regression and Time Series

    Hi, I'm in a college statistics course where I'm doing an assignement with Minitab. I have a one month time series of electricity use (hour intervals). I've attempted to remove the season effect from weekdays by index multiplication so all I'm left with (hopefully) is the effect from...
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    Mental math: Division of remainders

    tiny-tim, Thank you, I found a guide on Wikipedia that proved very helpful. HallsofIvy: Then I obviously didn't know long division, I didn't know you could use that to figure out the decimal value of the remainder. Your explanation helped. Thanks
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    Mental math: Division of remainders

    I'm working on moving away from long time slavery to the calculator Most forms of division and multiplication is going well now (long division and in some instances lattice multiplication) One thing I DON'T get though (and can't find any guides for) is dividing remainders. For example...
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    Cos(x): 8 in x's denominator

    ah, thanks I get it!
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    Cos(x): 8 in x's denominator

    I'm not getting it... :P
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    Cos(x): 8 in x's denominator

    I have (from a complex equation problem) found the following angles in the answers: 5PI/8, 9PI/8, 13PI/8, 17PI/8 In the same assignement I found sin(PI/8) = .5*sqrt(2-sqrt(2)) and I found the cos(PI/8) value by using standard trig. identities. Is there an easy way to use this result to...
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    Riemann sums

    Ok, so I have two questions regarding something I don't understand in my textbook (Adams) 1. 0 if 0<=x<1 or 1<x<=2 f(x) = 1 if x=1 (by "<=" i mean less than or equal) I'm supposed to show that it is Riemann integrable on that interval. They chose P to be: {0, 1-e/3...
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    Simple diff.eq

    Oh! sorry! I see it! bah hehe, the yx^2 messed up my head :P
  10. S

    Simple diff.eq

    Bah, sorry. I don't see what the integral of "dx^2y" evaluates to :(
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    Simple diff.eq

    Oh, thanks! Now I see it :)
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    Simple diff.eq

    Oh, but I didn't think I could do that when y*x^2 was encapsulated by parantheses. When I solve what you posted I get y=tan^-1(x) but the answer is supposed to be: (pi/4)(1/x^2)-(1/x)-tan^-1(x)/x^2 (the pi/4 comes from the start value...)
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    Simple diff.eq

    okey, I understand what you just wrote :P but I still don't know how to solve my problem...
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    Simple diff.eq

    Then I don't think we have learned about direct integration...
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    Simple diff.eq

    well, it's the d/dx(y*x^2) that confused me. we have only learned to solv the types: dy/dx=f(x)g(y) what is direct integration? Thanks
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    Simple diff.eq

    d/dx(y*x^2)=x^2/(1+x^2) I guess I can't write this as: dyx^2=x^2dx/(1+x^2) dy=dx/(1+x^2) beacuse I don't get the right answer... So what do I do?
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    Can someone show the steps?

    Oh, dear god... I can't believe I could be THAT silly :bugeye: Of course I see it, my incredible dull brain was confused by the n's, probably. Anyways, sorry for bothering you with this. That was rather embarrassing...
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    Can someone show the steps?

    Sorry, that's what I meant. Can you show me how you get to the right hand expression?
  19. S

    Can someone show the steps?

    how to go from: [(1+n)^n]/n to: (1+1/n)^n ?
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    Lagrange point

    oh, heh, I don't know what caused me to be so slow... I forgot the mass of the particle at the Lagrance point... Bah, sorry for the trouble :P
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    Lagrange point

    M=mass of earth m=mass of moon ?
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    Lagrange point

    but newtons gravitation law is yMm/r^2...
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    Lagrange point

    then what is the expression...?
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    Lagrange point

    but the product of the masses is the same on both sides right? dont they cancel...?
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    Lagrange point

    So im supposed to find the distance from the moon where the force on a particle from the earth and sun is equal. I get this expression (earth-moon distance is 400 000km): yMm/(r^2) = yMm / (400000km-r)^2 But from that I get r=200 000km and the answer should be 40 000km... whats wrong...
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    Can someone please explain the steps for me:

    = (1+x)^(-k-1) =1 / (1+x)^(k+1) Right?
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    Can someone please explain the steps for me:

    How can you go from: (1+x)^(k-1) / (1+x)^(2k) to: 1/ (1+x)^(k+1) ? Thanks!
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    Hints for integral

    Ok, thanks. I have that one now. Can you please hint me with one more: I have the integral of (sqrt(1-x^2)) / x^4 dx Which with trig.subs leads to: integral of cot^2(y) *csc^2(y) dy Again I'm stuck :P
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    Hints for integral

    Bah, I see it. I easily get confused when having to substitution i several steps :P Thanks
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