说下什么内容，列个目录也行啊，20个论坛币？

  谢谢楼主   还希望楼主多多分享呀

有点贵。

下来一看，貌似是一本概率论笔记，和大家上学时自己记的东西差不多。
没有目录，下面展示了第一章（希望楼主不要介意）：

18.05 Spring 2005 Lecture Notes
18.05 Lecture 1 February 2, 2005
Required Textbook -DeGroot & Schervish, “Probability and Statistics,” Third Edition Recommended Introduction to Probability Text -Feller, Vol. 1
§1.2-1.4. Probability, Set Operations.
What is probability?
•
Classical Interpretation: all outcomes have equal probability (coin, dice)
•
Subjective Interpretation (nature of problem): uses a model, randomness involved (such as weather)
– ex. drop of paint falls into a glass of water, model can describe P(hit bottom before sides) – or, P(survival after surgery)-“subjective,” estimated by the doctor.
•
Frequency Interpretation: probability based on history
– P(make a free shot) is based on history of shots made.
Experiment ↔has a random outcome.
1.
Sample Space -set of all possible outcomes. coin: S={H, T}, die: S={1, 2, 3, 4, 5,6}two dice: S={(i, j), i, j=1, 2, ..., 6}
2.
Events -any subset of sample space ex. A √S, A-collection of all events.
3.
Probability Distribution -P: A↔[0, 1] Event A √S, P(A) or Pr(A) -probability of A
Properties of Probability:
1.
0 ←P(A) ←1
2.
P(S) = 1
3.
For disjoint (mutually exclusive) events A, B (definition ↔A ∞B=
≥)
P(A or B) = P(A) + P(B) -this can be written for any number of events. For a sequence of events A1, ..., An, ... all disjoint (Ai ∞Aj = ≥, i = j):
∈
∗�∗�
P(
Ai) =
P(Ai)
i=1 i=1
which is called “countably additive.”
If continuous, can’t talk about P(outcome), need to consider P(set)
Example: S= [0,1],0 <a<b<1.
P([a,b]) = b−a,P(a) = P(b) = 0.
1
Need to group outcomes, not sum up individual points since they all have P = 0.
§1.3 Events, Set Operations
Union of Sets: A⇒ B= {s⊂ S: s⊂ Aor s⊂ B
}
Intersection: A∞ B= AB= {s⊂ S: s⊂ Aand s⊂ B
}
c
Complement: A= {s⊂ S: s/
⊂ A
}
Set Difference: A\ B= A− B= {s⊂ S: s⊂ Aand s/
⊂ B} = A∞ B
2
c
c
Symmetric Difference: (A∞ Bc) ⇒ (B∞ A)
Summary of Set Operations:
1. Union of Sets: A⇒ B= {s⊂ S: s⊂ Aor s⊂ B
}
2.
Intersection: A∞ B= AB= {s⊂ S: s⊂ Aand s⊂ B
3.
Complement: Ac = {s⊂ S: s/}
⊂ A
} c
4. Set Difference: A\ B= A− B= {s⊂ S: s⊂ Aand s/
⊂ B} = A∞ B
5. Symmetric Difference:
A⇔B= {s⊂ S: (s⊂ Aand s/) or (s⊂ Band s/
⊂ B⊂ A)} =
c)
(A∞ Bc) ⇒ (B∞ A
Properties of Set Operations:
1. AB= BA
⇒⇒
2. (A⇒ B) ⇒ C= A⇒ (BC)
⇒
Note that 1. and 2. are also valid for intersections.
3.
For mixed operations, associativity matters:
(A⇒ B) ∞ C= (A∞ C) ⇒ (B∞ C)
think of union as addition and intersection as multiplication: (A+B)C = AC + BC
c
4.
(A⇒ B)c = A∞ Bc -Can be proven by diagram below:
Both diagrams give the same shaded area of intersection.
c
5.
(A∞ B)c = ABc -Prove by looking at a particular point:
⇒
s⊂ (A∞ B)c = s/
⊂ (A∞ B)
cc
⊂ Aor s/s/⊂ B= s⊂ Aor s⊂ Bs⊂ (A
c Bc)
⇒
QED
** End of Lecture 1

顶 概率是基础。 有点贵撒
以前上概率课的时候觉得作业多又难，现在觉得是必须的