1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Exponential Density Function

  1. Apr 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Given f(x;λ) = [itex]cx^{2}e^{-λx}[/itex] for x ≥ 0

    Determine what c must be (as a function of λ) then determine the maximum likelihood estimator of λ.

    3. The attempt at a solution

    So i'm supposed to integrate this from 0 to infinity, from what i can gather.

    Let u = [itex]x^{2}[/itex], du = 2xdx, dv = [itex]e^{-λx}[/itex] and v = [itex]-e^{-λx} / λ[/itex]

    After a bit of work i end up with:

    -c/λ [ [itex]x^{2}e^{-λx}|_{0}^{∞} + 2( xe^{-λx}/λ |^{∞}_{0})[/itex] ]

    What throws me off is that evaluating this leaves me with -c/λ( 0 ), which has to be wrong...
  2. jcsd
  3. Apr 8, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    You have to integrate the second term from 0 to infinity, not just evaluate it. You'll need to integrate by parts again.
  4. Apr 8, 2013 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It might be easier to recognize that
    [tex] x e^{-\lambda x} = - \frac{\partial}{\partial \lambda} e^{- \lambda x}, [/tex]
    and so forth.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted