Introduction to Probability · 免费预览
和的矩母函数与概率生成函数
独立求和时矩母函数可以相乘，使卷积恒等式变得轻而易举；概率生成函数则为计数分布完成同样的记账工作。
1. MGFs multiply over independent sums
MGFs multiply over independent sums
2. Averages and the CLT seed
Averages and the CLT seed
3. The probability generating function
The probability generating function
4. The product rule's hypothesis
When does M of X plus Y equal M of X times M of Y?
5. Normal sums
X is Normal(2, 9) and Y is independent Normal(5, 16). What is the distribution of X + Y?
6. Summing Poissons
Independent counts X Poisson(2) and Y Poisson(7): the sum's MGF is e to the 2(e^t minus 1) times e to the 7(e^t minus 1). The sum is Poisson with what parameter? Enter an integer.
7. Averaging scales the argument
X has MGF M(t) = e^(3t + 2t^2), so each copy has mean 3. For the average of 2 independent copies, what is the mean? Enter like 3.
8. PGF first derivative
A PGF is G(s) = 0.2 + 0.5 s + 0.3 s squared. Compute G prime of 1, which equals E(X). Enter like 1.1.
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.