L' Hopital Rule Problem and MGFs Statistics

[thoradicus]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

Okay, this is an indeterminate equation.. that's 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 I am 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?

 

[Ray Vickson]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

Okay, this is an indeterminate equation.. that's 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 I am 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?

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.

 

[thoradicus]

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.

I stand corrected haha.

Can you elaborate abit on what you mean by expanding the numerator? Is it the expansion of the partial fractions?

 

[Ray Vickson]

I stand corrected haha.

Can you elaborate abit on what you mean by expanding the numerator? Is it the expansion of the partial fractions?

I mean: write out the series expansion of exp(5t) - exp(4t) in powers of t.

 

[thoradicus]

Oh are you talking about the Taylor's Series?

 

[Ray Vickson]

Oh are you talking about the Taylor's Series?

Don't keep asking---just go ahead and do it.

 

[Dick]

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.

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.