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    Hey,

    the queston is:
    The number of goals scored by a soccer team in a period of duration t minutes
    follows a Poisson distribution with mean t/36


    (i) Write down the probability that no goals are scored during a period of
    duration t minutes.
    X~Po(t/36), P(x=0) = e^(-t/36)

    (ii) The random variable T is defined as the length of time, in minutes, between
    successive goals. Show that T follows an exponential distribution.
    This part is where i am confused, how do i go about proving this?
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    Perhaps you could start with P(T>t)=P(\text{No\ goals\ in\ }t\text{\ minutes})=e^{\frac{-t}{36}} .
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    (Original post by meatball893)
    Perhaps you could start with P(T>t)=P(\text{No\ goals\ in\ }t\text{\ minutes})=e^{\frac{-t}{36}} .
    So P(T>t) = e^(-t/36)
    1 - P(T<t) = e^(-t/36)
    P(T<t) = 1 - e^(-t/36) = F(T)
    Derivative of F(T) => f(T) = (1/36)e^(-t/36)
    and therefore T follows an exponential distribution with mean = 1/36?
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    (Original post by Andre09)
    So P(T>t) = e^(-t/36)
    1 - P(T<t) = e^(-t/36)
    P(T<t) = 1 - e^(-t/36) = F(T)
    Derivative of F(T) => f(T) = (1/36)e^(-t/36)
    and therefore T follows an exponential distribution with mean = 1/36?
    Looks right to me
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    (Original post by meatball893)
    Looks right to me
    awesome, thanks for the help
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    Welcome
 
 
 
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