Introduction to Probability · 免费预览
几何分布与负二项分布：等待分布
等待首次成功与第 r 次成功：依情境推导它们的 PMF，用首步分析法求期望，以及无记忆性质。
1. The Geometric story
The Geometric story
2. Expectation by first-step analysis
Expectation by first-step analysis
3. Negative Binomial and the r-th success
Negative Binomial and the r-th success
4. Memorylessness
Memorylessness
5. A geometric tail
A shooter hits with probability 0.2 per independent shot. What is the probability the first hit takes more than 5 shots?
6. Memorylessness in action
A website gets an order with probability 0.1 each independent minute. Forty quiet minutes have passed. What is the probability the next order takes more than 10 more minutes?
7. Expected wait
A rare event has probability 0.004 per independent trial. On average, how many trials until the first occurrence? Enter a number like 250.
8. Negative Binomial mean
Waiting for the 3rd success with per-trial probability 0.25, the expected total number of trials is r/p. Enter that integer.
9. Coupon stage
Collecting coupons, you have 4 of 5 kinds. Each box independently gives any kind with probability 1/5. The expected number of boxes to get the last missing kind is what number? Enter like 5.
10. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.