Stochastic Processes · 免费预览
定义泊松过程
泊松分布用于计数罕见且相互独立的事件，其均值与方差相同，相互独立的泊松分布相加后仍为泊松分布；而泊松过程是这样的计数过程：其在长度为 t 的区间上的增量相互独立，且均服从均值为速率乘以 t 的泊松分布。
1. A distribution for counting rare events
A distribution for counting rare events
2. From many rare chances to the limit
From many rare chances to the limit
3. The counting process definition
The counting process definition
4. Computing with rate times time
Computing with rate times time
5. The matching of mean and variance
For a Poisson random variable with mean lambda, what is its variance?
6. Independent counts add
Mail-order calls arrive as a Poisson process of rate 3 per hour, walk-ins as an independent process of rate 2 per hour. What is the distribution of the total number of customers in one hour?
7. The three defining properties
Which three conditions define a Poisson process of rate lambda?
8. Reading the staircase
The process is built from interarrival times tau and arrival epochs T. What does the event N of s equal n say about the arrival epochs?
9. Restarting at a fixed time
Why does a Poisson process have independent increments over disjoint intervals?
10. Units are the classic trap
Arrivals occur at rate 3 per hour. What is the distribution of the number of arrivals in forty minutes?
11. A quiet hour
Customers arrive at rate 3 per hour as a Poisson process. Compute the probability of zero arrivals in one hour and write the answer as a decimal.
12. Exactly two shoppers
For the same rate 3 per hour Poisson process, compute the probability of exactly two arrivals in one hour and write the answer as a decimal.
13. Waiting for the third knock
For a Poisson process of rate 3 per hour, the third arrival time is the sum of three independent exponential interarrival times. Compute its expected value in hours and write the number.