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Likelihood Function - Exponential Distribution

  1. Feb 16, 2009 #1
    1. The problem statement, all variables and given/known data
    X is exponentially distributed. 3 observations are made by an instrument that reports x1=5, x2=3, but x3 is too large for the instrument to measure and it reports only that x3 > 20 . (The largest value the instrument can measure is 10)

    a)What is the likelihood function?
    b)What is the mle of t?


    2. Relevant equations
    f(x;t)=t*exp(-t*x), E(X)=1/t ,
    F(x) = P(X<=x)=1-exp(-t*x)

    3. The attempt at a solution
    a)(t^3)*exp(-3t*(avg of X))
    b) take natural log of a), take derivative, then set equal to 0 and solve for t

    Wondering if I am on the right track?
    Thanks
     
  2. jcsd
  3. Feb 20, 2009 #2
    I've answered your other topic.
     
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