Introduction to Probability · 免费预览
马尔可夫链与转移矩阵
下一步仅依赖于当前状态的过程，其完整描述是转移矩阵，而多步演化则通过矩阵幂来实现。
1. The Markov property
The Markov property
2. Evolving the chain
Evolving the chain
3. Where Markov models come from
Where Markov models come from
4. The Markov property's meaning
For a Markov chain, given the current state, the past provides what additional information about the next state?
5. Reading a transition matrix
In a transition matrix Q, the entry in row i, column j equals what?
6. One-step evolution
From state A, the chain goes to A with probability 0.7 and B with 0.3. From B it goes to A with 0.4 and B with 0.6. Starting certainly at A, what is P(at A after one step)? Enter a decimal like 0.7.
7. Two-step probability
With the same chain, starting at A, the two-step probability of being back at A is 0.7 times 0.7 plus 0.3 times 0.4. Compute it. Enter like 0.61.
8. First-step equation anchor
A gambler at fortune 1 plays to 3, moving up or down with probability 1/2 each round, absorbing at 0 and 3. The first-step equations are E_1 = 1 + one half E_2, E_2 = 1 + one half E_1, with E_0 = E_3 = 0. What is E_1? Enter an integer.
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.