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Homework Help: Me! the variance of the score function in exponential distribution

  1. Sep 20, 2010 #1
    plz help me! the variance of the score function in exponential distribution

    1. The problem statement, all variables and given/known data

    My question is about exponential function, with its density function known as

    f(x;theta) = (1/theta) e^(-x/theta) for all x>0.

    where E(x) = theta, var(x) = theta^2

    My question is, what is E( [d ln(theta) / d(theta)}^2]?

    2. Relevant equations

    As you see, the question provided the variance and expected value for X, but not Theta.

    I calculated theta's MLE for the previous queston.. am i supposed to use it somehow?

    3. The attempt at a solution

    I have been stuck with this one particular question over this weekend, and
    unluckily I could not figure it out by myself. If you can help me a bit with this problem,
    I will really really appreciate it.

    I set up a likelihood function, and I was able to get the equation for the
    d ln(theta) / d(theta).

    it was:

    d ln(theta)/d(theta) = -T/(theta) + 1/{(theta)^2} sigma(t=1 to t=T) Xt

    since E(x^2) = var(x) + [e(x)]^2

    and the score is zero, then what i am looking for is must be equal to var(x),

    which is var(-T/(theta) + 1/{(theta)^2} sigma(t=1 to t=T) Xt)

    it has bunch of stuffs inside, and i am really confused. the question didnt provide

    any information of var(theta).. i mean i calculated MLE for theta, but i am not sure

    if i can plug in this equation.

    can someone please help me out with this one question?
  2. jcsd
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