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Math Help - exponential distrubtion

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    exponential distrubtion

    I have no idea about this, i hope that someone can help me.
    If the number of minutes that a doctor spends with a patient is a random variable having an exponential distrubtion with the a=9, what are the probabilities that it will take the doctor at least 20 minutes to treat one patient?
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    Hello,
    Quote Originally Posted by yuan.69 View Post
    I have no idea about this, i hope that someone can help me.
    If the number of minutes that a doctor spends with a patient is a random variable having an exponential distrubtion with the a=9, what are the probabilities that it will take the doctor at least 20 minutes to treat one patient?
    Let X be the random variable representing the time the doctor spends with a patient.

    You are looking for P(X \geqslant 20)
    This is 1-P(X < 20)=1-P(X \leqslant 20)

    But you surely know the cumulative distribution function of the exponential distribution, don't you ?
    P(X \leqslant x)=F(x)=1-e^{-\lambda x}, for positive x.
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