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Math Help - Exponential distribution with an unknown parameter, theta

  1. #1
    Senior Member chella182's Avatar
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    Exponential distribution with an unknown parameter, theta

    I don't actually know what topic this falls under exactly to be honest. The question goes:

    In an experiment to study pulses along a nerve fibre, the times between 101 successive pulses were measured. The n=100 observations gave a sample mean \bar{x}=26.05 seconds. Assuming that these data are a random sample from an exponential Exp(\theta) distribution, calculate

    (i) the most likely value for the mean pulse rate \theta per second

    (ii) the most likely value for the probability \phi that the time between successive pulses is greater than 20 seconds i.e. \phi=P(X>20)=e^{-20\theta}.
    Last edited by chella182; April 29th 2009 at 06:12 PM.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by chella182 View Post
    I don't actually know what topic this falls under exactly to be honest. The question goes:

    In an experiment to study pulses along a nerve fibre, the times between 101 successive pulses were measured. The n=100 observations gave a sample mean \bar{x}=26.05 seconds. Assuming that these data are a random sample from an exponential Exp(\theta) distribution, calculate

    (i) the most likely value for the mean pulse rate \theta per second


    (ii) the most likely value for the probability \phi that the time between successive pulses is greater than 20 seconds i.e. \phi=P(X>20)=e^{-20\theta}.
    Use the sample mean as an estimator of the mean for the exponential distribution.

    \Pr(\theta > 20) = \int_{20}^{+\infty} f(\theta) \, d \theta where f(\theta) is the pdf.
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  3. #3
    Senior Member chella182's Avatar
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    I don't remember learning this at all nothing like this is in my notes.

    Why integrate between 20 and \infty?
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