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Homework Help: Maximum Likelihood Estimator

  1. Nov 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose X1...Xn are iid and have PDF [tex]f(x; \theta) = \frac{1}{\theta} e^{\frac{-x}{\theta}} \ \ \ 0<x<\infty[/tex]

    Find the MLE of P(X<2).
    2. Relevant equations

    3. The attempt at a solution

    I know the MLE of theta is [tex]\overline{X}[/tex]

    so would [tex]P(X<2) = 1 - \frac{1}{\overline{X}} e^{\frac{-2}{\overline{X}}}[/tex]?

    Thank you in advance.
  2. jcsd
  3. Nov 25, 2009 #2
    nope, i think you should use the integral of pdf. the pdf is like the puntual probability of value x.
  4. Nov 25, 2009 #3
    you mean:

    [tex]1 - e^{\frac{-2}{\overline{X}}}[/tex]
  5. Nov 26, 2009 #4
    correct, i think
  6. Nov 26, 2009 #5
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