Introduction to Probability · 免费预览
叠加、抽稀、条件化与高维情形
合并独立过程、按标签拆分、以计数为条件，以及平面内的泊松点，并讨论检查悖论与公交车悖论。
1. Superposition and thinning
Superposition and thinning
2. Conditioning on a shared count
Conditioning on a shared count
3. Spatial Poisson processes
Spatial Poisson processes
4. Merging two streams
Independent processes of rates 2 and 5 merge. What is the merged stream?
5. Thinning a stream
A rate-6 process thins with p = 1/3 to type 1. What is the type-1 process?
6. A merged quiet window
Two independent processes of rates 1 and 2 per hour merge. What is P(no arrivals in a 30-minute window)? Use e^(-1.5) is about 0.223. Enter like 0.223.
7. Labels given the total
A merged stream of rates 2 and 6 has exactly 4 arrivals in a window. The number of type-1 (rate-2) arrivals is Binomial(4, p). What is p? Enter a fraction like 1/4.
8. Nearest star survival
Stars scatter at intensity 40 per square degree. P(no star within radius 0.1 degrees of a point) is e to the minus 40 pi times 0.1 squared. Using pi about 3.14, compute the exponent's value, like 1.26.
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.