Regarding Poisson process
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The number of cars which pass a roadside speed camera are assumed to behave as a Poisson process with intensity λ. It is found that the probability that a car exceeds the designated speed limit is p.
Show that the number of cars which break the speed limit also form a Poisson process.
If n cars pass the camera in time t, find the probability function for the number of cars which exceed the speed limit.
probability-theory statistics probability-distributions stochastic-processes stochastic-integrals
edited Nov 14 at 9:59
Bernard
115k637108
asked Nov 14 at 8:47
jass
235
add a comment |
up vote
0
down vote
favorite
I would like to ask how to do this question
The number of cars which pass a roadside speed camera are assumed to behave as a Poisson process with intensity λ. It is found that the probability that a car exceeds the designated speed limit is p.
Show that the number of cars which break the speed limit also form a Poisson process.
If n cars pass the camera in time t, find the probability function for the number of cars which exceed the speed limit.
probability-theory statistics probability-distributions stochastic-processes stochastic-integrals
edited Nov 14 at 9:59
Bernard
115k637108
asked Nov 14 at 8:47
jass
235
What have you tried ? Where are you stuck ?
– Tom-Tom
Nov 14 at 9:16
i didnt know how to start
– jass
Nov 14 at 9:20
can you provide me some steps to follow? thank you
– jass
Nov 14 at 9:21
You could start with computing $mathbb P(m|n)$ where $n$ is the number of cars passing during a fixed time $t$ and $m$ is the number of cars exceeding the speed limit.
– Tom-Tom
Nov 14 at 9:24
Here you assume you have a Poisson process of rate $lambda$ and each arrival is (independently, which should have been stated) special with probability $p$. A standard "Poisson splitting" fact says that the special arrivals also form a Poisson process (with smaller rate $lambda p$). The pre-requisites for your question are unknown so we cannot tell if you are meant to prove the general Poisson splitting rule, or just apply it. The second question has nothing to do with Poisson processes, it just asks about having $n$ things, each of which is independently special with prob $p$.
– Michael
Nov 14 at 15:26
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I would like to ask how to do this question
The number of cars which pass a roadside speed camera are assumed to behave as a Poisson process with intensity λ. It is found that the probability that a car exceeds the designated speed limit is p.
Show that the number of cars which break the speed limit also form a Poisson process.
If n cars pass the camera in time t, find the probability function for the number of cars which exceed the speed limit.
probability-theory statistics probability-distributions stochastic-processes stochastic-integrals
edited Nov 14 at 9:59
Bernard
115k637108
asked Nov 14 at 8:47
jass
235
I would like to ask how to do this question
The number of cars which pass a roadside speed camera are assumed to behave as a Poisson process with intensity λ. It is found that the probability that a car exceeds the designated speed limit is p.
Show that the number of cars which break the speed limit also form a Poisson process.
If n cars pass the camera in time t, find the probability function for the number of cars which exceed the speed limit.
probability-theory statistics probability-distributions stochastic-processes stochastic-integrals
probability-theory statistics probability-distributions stochastic-processes stochastic-integrals
edited Nov 14 at 9:59
Bernard
115k637108
asked Nov 14 at 8:47
jass
235
edited Nov 14 at 9:59
Bernard
115k637108
asked Nov 14 at 8:47
jass
235
edited Nov 14 at 9:59
Bernard
115k637108
edited Nov 14 at 9:59
Bernard
115k637108
edited Nov 14 at 9:59
Bernard
115k637108
115k637108
asked Nov 14 at 8:47
jass
235
asked Nov 14 at 8:47
jass
235
asked Nov 14 at 8:47
jass
235
235
What have you tried ? Where are you stuck ?
– Tom-Tom
Nov 14 at 9:16
i didnt know how to start
– jass
Nov 14 at 9:20
can you provide me some steps to follow? thank you
– jass
Nov 14 at 9:21
You could start with computing $mathbb P(m|n)$ where $n$ is the number of cars passing during a fixed time $t$ and $m$ is the number of cars exceeding the speed limit.
– Tom-Tom
Nov 14 at 9:24
Here you assume you have a Poisson process of rate $lambda$ and each arrival is (independently, which should have been stated) special with probability $p$. A standard "Poisson splitting" fact says that the special arrivals also form a Poisson process (with smaller rate $lambda p$). The pre-requisites for your question are unknown so we cannot tell if you are meant to prove the general Poisson splitting rule, or just apply it. The second question has nothing to do with Poisson processes, it just asks about having $n$ things, each of which is independently special with prob $p$.
– Michael
Nov 14 at 15:26
add a comment |
What have you tried ? Where are you stuck ?
– Tom-Tom
Nov 14 at 9:16
i didnt know how to start
– jass
Nov 14 at 9:20
can you provide me some steps to follow? thank you
– jass
Nov 14 at 9:21
You could start with computing $mathbb P(m|n)$ where $n$ is the number of cars passing during a fixed time $t$ and $m$ is the number of cars exceeding the speed limit.
– Tom-Tom
Nov 14 at 9:24
Here you assume you have a Poisson process of rate $lambda$ and each arrival is (independently, which should have been stated) special with probability $p$. A standard "Poisson splitting" fact says that the special arrivals also form a Poisson process (with smaller rate $lambda p$). The pre-requisites for your question are unknown so we cannot tell if you are meant to prove the general Poisson splitting rule, or just apply it. The second question has nothing to do with Poisson processes, it just asks about having $n$ things, each of which is independently special with prob $p$.
– Michael
Nov 14 at 15:26
What have you tried ? Where are you stuck ?
– Tom-Tom
Nov 14 at 9:16
What have you tried ? Where are you stuck ?
– Tom-Tom
Nov 14 at 9:16
i didnt know how to start
– jass
Nov 14 at 9:20
i didnt know how to start
– jass
Nov 14 at 9:20
can you provide me some steps to follow? thank you
– jass
Nov 14 at 9:21
can you provide me some steps to follow? thank you
– jass
Nov 14 at 9:21
You could start with computing $mathbb P(m|n)$ where $n$ is the number of cars passing during a fixed time $t$ and $m$ is the number of cars exceeding the speed limit.
– Tom-Tom
Nov 14 at 9:24
You could start with computing $mathbb P(m|n)$ where $n$ is the number of cars passing during a fixed time $t$ and $m$ is the number of cars exceeding the speed limit.
– Tom-Tom
Nov 14 at 9:24
Here you assume you have a Poisson process of rate $lambda$ and each arrival is (independently, which should have been stated) special with probability $p$. A standard "Poisson splitting" fact says that the special arrivals also form a Poisson process (with smaller rate $lambda p$). The pre-requisites for your question are unknown so we cannot tell if you are meant to prove the general Poisson splitting rule, or just apply it. The second question has nothing to do with Poisson processes, it just asks about having $n$ things, each of which is independently special with prob $p$.
– Michael
Nov 14 at 15:26
Here you assume you have a Poisson process of rate $lambda$ and each arrival is (independently, which should have been stated) special with probability $p$. A standard "Poisson splitting" fact says that the special arrivals also form a Poisson process (with smaller rate $lambda p$). The pre-requisites for your question are unknown so we cannot tell if you are meant to prove the general Poisson splitting rule, or just apply it. The second question has nothing to do with Poisson processes, it just asks about having $n$ things, each of which is independently special with prob $p$.
– Michael
Nov 14 at 15:26
add a comment |
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What have you tried ? Where are you stuck ?
– Tom-Tom
Nov 14 at 9:16
i didnt know how to start
– jass
Nov 14 at 9:20
can you provide me some steps to follow? thank you
– jass
Nov 14 at 9:21
You could start with computing $mathbb P(m|n)$ where $n$ is the number of cars passing during a fixed time $t$ and $m$ is the number of cars exceeding the speed limit.
– Tom-Tom
Nov 14 at 9:24
Here you assume you have a Poisson process of rate $lambda$ and each arrival is (independently, which should have been stated) special with probability $p$. A standard "Poisson splitting" fact says that the special arrivals also form a Poisson process (with smaller rate $lambda p$). The pre-requisites for your question are unknown so we cannot tell if you are meant to prove the general Poisson splitting rule, or just apply it. The second question has nothing to do with Poisson processes, it just asks about having $n$ things, each of which is independently special with prob $p$.
– Michael
Nov 14 at 15:26