Introduction to Probability · 免费预览
贝塔分布与伽马分布：顺序敏感的分布族
在 [0, 1] 上的贝塔分布族与在 [0, 无穷大] 上的伽马分布族、它们的概率情境、参数的影响，以及贝塔分布与二项分布之间的衔接。
1. The Beta family
The Beta family
2. The Gamma family
The Gamma family
3. The bridges
The bridges
4. Reading Beta parameters
A Beta(a, b) has a = 20 and b = 5. Where does its mass sit?
5. Gamma mean by story
A Poisson process of rate 3 per minute runs until its 4th arrival. What is the expected total wait?
6. Beta mean
X is Beta(3, 9). What is the mean? Enter a decimal like 0.25.
7. Conjugate update
A Beta(2, 2) prior on a coin's bias updates with data of 5 heads and 1 tail. The posterior is Beta with what two parameters? Enter the first parameter only.
8. Chi-square as Gamma
Chi-square with k degrees of freedom is Gamma with shape k/2 and rate 1/2. For Chi-square(10), what is the mean? Enter an integer.
9. Beta-Gamma share
X is Gamma(2, 1) and Y is Gamma(3, 1), independent. The share X/(X+Y) is Beta with parameters 2 and 3. What is its expected value? Enter like 0.4.
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.