Introduction to Probability · 免费预览
状态的分类：常返态与暂态
不可约性、常返性与暂留性之别、吸收概率，以及通过首步分析系统计算的期望吸收时间。
1. Communication and irreducibility
Communication and irreducibility
2. Recurrent and transient states
Recurrent and transient states
3. Canonical form and applications
Canonical form and applications
4. Identifying a transient class
A finite chain's class has an arrow leaving it. What is its classification?
5. Recurrent means what?
Starting at a recurrent state i in a finite chain, what happens with probability 1?
6. Expected visits to a transient state
From transient state s, each step independently exits the system forever with probability 0.1, otherwise revisits are possible. The number of visits to s is geometric with success, exit, probability 0.1. What is the expected number of visits? Enter an integer.
7. Absorption time anchor
An absorbing chain has E at the absorbing state equal to 0 by anchor, and E at a transient state equal 1 plus 0.5 times E at the absorbing state plus 0.5 times E back at itself. Solve: E = 1 + 0.5 E, so E equals what? Enter an integer.
8. Ruin probability edge
A gambler plays until 0 or 4, up-probability 0.5. By symmetry the ruin probability from fortune 2 is exactly what? Enter a decimal like 0.5.
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.