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# Poisson and exponential distribution watch

1. 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?
3. (Original post by meatball893)
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?
4. (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
5. (Original post by meatball893)
Looks right to me
awesome, thanks for the help
6. Welcome

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