h**********y
发帖数: 41 | 1 You are waiting for a bus at station. If the buses have an average arrival
time of 10 minutes and you arrive at the bus station at a random time. What
is your expected waiting time if the buses arrive according to a uniform
distribution? If you have waited for 2 minutes, how many more minutes do you
expect to wait?
绿书里给出了Poisson process的解法，但我想知道这类题目更一般的解法，如果换成
是uniform distribution 或其他将怎么解呢？ |
k*****y
发帖数: 744 | 2 请问如何定义buses arrival according to a uniform distribution?
Poisson process是从N(t) = # of arrivals at t开始定义，然后可以推出based on任
意时刻a，下一辆车到达的时间差是exponetial分布，跟时刻a无关，相当于memoryless
。所以expected waiting time可以make sense。
反过来定义的话，如果要得到memoryless的uniform似乎不是well defined的。
What
you
【在 h**********y 的大作中提到】
: You are waiting for a bus at station. If the buses have an average arrival
: time of 10 minutes and you arrive at the bus station at a random time. What
: is your expected waiting time if the buses arrive according to a uniform
: distribution? If you have waited for 2 minutes, how many more minutes do you
: expect to wait?
: 绿书里给出了Poisson process的解法，但我想知道这类题目更一般的解法，如果换成
: 是uniform distribution 或其他将怎么解呢？
|
i**w
发帖数: 71 | 3 绿皮书上有提到，residual time和对应的reference.我还被问到过一次。
【在 h**********y 的大作中提到】
: You are waiting for a bus at station. If the buses have an average arrival
: time of 10 minutes and you arrive at the bus station at a random time. What
: is your expected waiting time if the buses arrive according to a uniform
: distribution? If you have waited for 2 minutes, how many more minutes do you
: expect to wait?
: 绿书里给出了Poisson process的解法，但我想知道这类题目更一般的解法，如果换成
: 是uniform distribution 或其他将怎么解呢？
|
c********d
发帖数: 173 | 4
memoryless
【在 k*****y 的大作中提到】
: 请问如何定义buses arrival according to a uniform distribution?
: Poisson process是从N(t) = # of arrivals at t开始定义，然后可以推出based on任
: 意时刻a，下一辆车到达的时间差是exponetial分布，跟时刻a无关，相当于memoryless
: 。所以expected waiting time可以make sense。
: 反过来定义的话，如果要得到memoryless的uniform似乎不是well defined的。
:
: What
: you
|
c********d
发帖数: 173 | 5 他意思是interarrival time是uniformly distributed
定义没有问题的。
memoryless
【在 k*****y 的大作中提到】
: 请问如何定义buses arrival according to a uniform distribution?
: Poisson process是从N(t) = # of arrivals at t开始定义，然后可以推出based on任
: 意时刻a，下一辆车到达的时间差是exponetial分布，跟时刻a无关，相当于memoryless
: 。所以expected waiting time可以make sense。
: 反过来定义的话，如果要得到memoryless的uniform似乎不是well defined的。
:
: What
: you
|
R**T
发帖数: 784 | 6 我这认为这个题对于非memoryless的分布并不是well-defined
具体来说我觉得"the guest arrives at the train station randomly"这个randomly
不好定义
memoryless
【在 k*****y 的大作中提到】
: 请问如何定义buses arrival according to a uniform distribution?
: Poisson process是从N(t) = # of arrivals at t开始定义，然后可以推出based on任
: 意时刻a，下一辆车到达的时间差是exponetial分布，跟时刻a无关，相当于memoryless
: 。所以expected waiting time可以make sense。
: 反过来定义的话，如果要得到memoryless的uniform似乎不是well defined的。
:
: What
: you
|
