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?
probability poisson-distribution
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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?
probability poisson-distribution
add a comment |Â
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?
probability poisson-distribution
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
probability poisson-distribution
edited Sep 7 at 13:27
asked Sep 7 at 11:20
user585380
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556
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1 Answer
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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 $E[X_1+X_2]$.
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 $E[X_1+X_2]$.
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
add a comment |Â
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 $E[X_1+X_2]$.
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
add a comment |Â
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 $E[X_1+X_2]$.
- 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 $E[X_1+X_2]$.
answered Sep 7 at 11:24
Siong Thye Goh
82.7k1456104
82.7k1456104
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
add a comment |Â
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
So, will that be 1/2 + 1/2?
â user585380
Sep 7 at 13:25
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
yes, that is how you get $1$.
â Siong Thye Goh
Sep 7 at 14:56
add a comment |Â
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