Introduction to Probability · 免费预览
一维泊松过程
通过计数与公理给出的形式化定义、指数型到达间隔结构、到达时间的次序统计量，以及非齐次速率。
1. The process, defined
The process, defined
2. Arrival times and order statistics
Arrival times and order statistics
3. Nonhomogeneous rates
Nonhomogeneous rates
4. Counting in a window
Arrivals form a Poisson process of rate 4 per hour. What is the distribution of arrivals in a 90-minute window?
5. Conditioned on the count
Given exactly 3 arrivals in [0, 1] from a rate-2 Poisson process, what is the distribution of the arrival times?
6. Integrated intensity
A nonhomogeneous process has rate lambda(t) = 3t arrivals per hour. What is the expected count in the first 2 hours, the integral from 0 to 2 of 3t dt? Enter an integer.
7. First wait probability
For a rate-2 per hour process, what is P(first arrival takes more than half an hour)? Use e^(-1) is about 0.368. Enter like 0.368.
8. Third arrival mean
The k-th arrival of a rate-3 process has Gamma(k, 3) distribution with mean k over lambda. What is the expected time of the third arrival? Enter like 1.0.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.