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L' Hopital Rule Problem and MGFs Statistics

  1. Oct 14, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey all, been having some problem with the rule..technique looks right but doesn't agree with wolfram's calc answer. Doing a moment generating function problem.

    M(t)=(e^5t-e^4t)/t, Find EX and VARX


    2. Relevant equations
    M'(0)=e(x) and so on..


    3. The attempt at a solution
    Okay, this is an indeterminate equation.. thats why I had to use this rule.. But my answer keeps getting 9 while wolfram says 9/2, so I need some help here.

    Ok, using quotient rule, differentiating, I get (5e^5t-4e^4t)/t + (e^4t-e^5t)/t^2. Correct me if Im wrong.

    I separated the latter part of the equation into ((e^4t-e^5t)/t)(1/t), which then equals to (-1)(1/t)

    Therefore, I get (5e^5t-4e^4t-1)/t, which is indeterminate again, differentiating both nominators, i get 9. What have I done wrong?
     
  2. jcsd
  3. Oct 14, 2013 #2

    Ray Vickson

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    Using l'Hospital's rule is much harder than what you need. Just expand the numerator in powers of t and see what you get.

    BTW: the correct spelling is l'Hospital (yes, like the place you go to for medical help)---not l'Hopital. It is pronounced low-pee-tall but not spelled that way.
     
  4. Oct 14, 2013 #3
    I stand corrected haha.

    Can you elaborate abit on what you mean by expanding the numerator? Is it the expansion of the partial fractions?:confused:
     
  5. Oct 14, 2013 #4

    Ray Vickson

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    I mean: write out the series expansion of exp(5t) - exp(4t) in powers of t.
     
  6. Oct 15, 2013 #5
    Oh are you talking about the Taylor's Series?
     
  7. Oct 15, 2013 #6

    Ray Vickson

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    Don't keep asking---just go ahead and do it.
     
  8. Oct 15, 2013 #7

    Dick

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    I would say if the French can drop pronounciation of consonants and replace them with circumflex accents then it's perfectly ok for English speakers to replace that with l'Hopital. Since we don't use those accents. This is really fussy. It reflects the current pronunciation better.
     
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