Introduction to Probability · 免费预览
泊松分布及其与二项分布的联系
在固定窗口内对罕见事件计数、泊松分布的概率质量函数及其源自二项分布的稀有事件极限定理，以及泊松分布的条件分解。
1. The Poisson story
The Poisson story
2. The law of rare events
The law of rare events
3. Thinning and splitting
Thinning and splitting
4. Poisson mean and variance
A website's hourly error count is Poisson with mean 4. What is the standard deviation?
5. When the Poisson approximation fits
Which count is the best candidate to model as Poisson?
6. A clean page
A server averages 3 failed requests per hour, modeled as Poisson. What is the probability an hour has zero failures? Round to three decimals, like 0.050.
7. Rare disease count
A condition affects 2 per 100,000 people independently. In a city of 400,000, the expected number of cases is what number? Enter like 8.
8. Thinning a stream
Emails arrive at Poisson rate 20 per hour, and independently 1 in 4 is spam. The spam count per hour is Poisson with what parameter? Enter like 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.