Poisson distribution car crash

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Car crashes at a traffic stop arrive follows a Poisson Process with rate lambda = 2/hr.



(a) Expected amount of time until the 2nd car crash arrives



Why is the expected amount of time until the second car crash is 1 hour? How did we get that number?



b) If car crashes arrive at another traffic stop according to Poisson Process with rate 3/hr, find expected time we wait until a car crash occurs at either traffic stop. Why is this 1/5?










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    Car crashes at a traffic stop arrive follows a Poisson Process with rate lambda = 2/hr.



    (a) Expected amount of time until the 2nd car crash arrives



    Why is the expected amount of time until the second car crash is 1 hour? How did we get that number?



    b) If car crashes arrive at another traffic stop according to Poisson Process with rate 3/hr, find expected time we wait until a car crash occurs at either traffic stop. Why is this 1/5?










    share|cite|improve this question

























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Car crashes at a traffic stop arrive follows a Poisson Process with rate lambda = 2/hr.



      (a) Expected amount of time until the 2nd car crash arrives



      Why is the expected amount of time until the second car crash is 1 hour? How did we get that number?



      b) If car crashes arrive at another traffic stop according to Poisson Process with rate 3/hr, find expected time we wait until a car crash occurs at either traffic stop. Why is this 1/5?










      share|cite|improve this question















      Car crashes at a traffic stop arrive follows a Poisson Process with rate lambda = 2/hr.



      (a) Expected amount of time until the 2nd car crash arrives



      Why is the expected amount of time until the second car crash is 1 hour? How did we get that number?



      b) If car crashes arrive at another traffic stop according to Poisson Process with rate 3/hr, find expected time we wait until a car crash occurs at either traffic stop. Why is this 1/5?







      probability poisson-distribution






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      edited Sep 7 at 13:27

























      asked Sep 7 at 11:20









      user585380

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          • Remember that for a poisson process, the interarrival time follows exponential distribution with mean $frac1lambda$.

          Let $X_1$ be the time until the first crash and let $X_2$ be the time until the second crash from the first crash.



          You just have to compute $E[X_1+X_2]$.






          share|cite|improve this answer




















          • So, will that be 1/2 + 1/2?
            – user585380
            Sep 7 at 13:25










          • yes, that is how you get $1$.
            – Siong Thye Goh
            Sep 7 at 14:56










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          1 Answer
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          1 Answer
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          up vote
          0
          down vote













          • Remember that for a poisson process, the interarrival time follows exponential distribution with mean $frac1lambda$.

          Let $X_1$ be the time until the first crash and let $X_2$ be the time until the second crash from the first crash.



          You just have to compute $E[X_1+X_2]$.






          share|cite|improve this answer




















          • So, will that be 1/2 + 1/2?
            – user585380
            Sep 7 at 13:25










          • yes, that is how you get $1$.
            – Siong Thye Goh
            Sep 7 at 14:56














          up vote
          0
          down vote













          • Remember that for a poisson process, the interarrival time follows exponential distribution with mean $frac1lambda$.

          Let $X_1$ be the time until the first crash and let $X_2$ be the time until the second crash from the first crash.



          You just have to compute $E[X_1+X_2]$.






          share|cite|improve this answer




















          • So, will that be 1/2 + 1/2?
            – user585380
            Sep 7 at 13:25










          • yes, that is how you get $1$.
            – Siong Thye Goh
            Sep 7 at 14:56












          up vote
          0
          down vote










          up vote
          0
          down vote









          • Remember that for a poisson process, the interarrival time follows exponential distribution with mean $frac1lambda$.

          Let $X_1$ be the time until the first crash and let $X_2$ be the time until the second crash from the first crash.



          You just have to compute $E[X_1+X_2]$.






          share|cite|improve this answer












          • Remember that for a poisson process, the interarrival time follows exponential distribution with mean $frac1lambda$.

          Let $X_1$ be the time until the first crash and let $X_2$ be the time until the second crash from the first crash.



          You just have to compute $E[X_1+X_2]$.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Sep 7 at 11:24









          Siong Thye Goh

          82.7k1456104




          82.7k1456104











          • So, will that be 1/2 + 1/2?
            – user585380
            Sep 7 at 13:25










          • yes, that is how you get $1$.
            – Siong Thye Goh
            Sep 7 at 14:56
















          • So, will that be 1/2 + 1/2?
            – user585380
            Sep 7 at 13:25










          • yes, that is how you get $1$.
            – Siong Thye Goh
            Sep 7 at 14:56















          So, will that be 1/2 + 1/2?
          – user585380
          Sep 7 at 13:25




          So, will that be 1/2 + 1/2?
          – user585380
          Sep 7 at 13:25












          yes, that is how you get $1$.
          – Siong Thye Goh
          Sep 7 at 14:56




          yes, that is how you get $1$.
          – Siong Thye Goh
          Sep 7 at 14:56

















           

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