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Ryan 2023-06-16 20:40:38 +08:00
parent 6454faa2ce
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@ -2609,6 +2609,8 @@
CLOCK: [2023-06-03 Sat 16:47:39]--[2023-06-03 Sat 16:47:40] => 00:00:01
:END:
- LATER Mind map
deck:: 2023t1/math
collapsed:: true
:LOGBOOK:
CLOCK: [2023-06-16 Fri 15:00:23]--[2023-06-16 Fri 15:18:37] => 00:18:14
:END:
@ -2693,28 +2695,57 @@
- ((648c2860-5454-45f1-80f8-1c85bce84fd1))
- ((648c290a-3532-4e56-8536-258daf7b00a7))
- Distribution Function
collapsed:: true
- ((648c2970-9091-4f46-8745-b0c10cdeb832))
collapsed:: true
- ((648c2994-36eb-44bf-8038-e49d2390a5b0))
- ((648c2a73-3961-4723-90e8-5f160bb18e0d)) ![section 2.2.pdf](../assets/section_2.2_1686907456219_0.pdf)
collapsed:: true
- ((648c2a88-3d0f-47d2-be44-21df002a1def))
- ((648c2abf-5c5e-4af9-9e13-bb566f3206e8))
- ((648c2b26-e92d-43f7-b8e1-60b51a2b5268))
- Discrete type
collapsed:: true
- Definition: ((648c2be0-787e-4e1f-8d0c-b859f0d08383))
- Continuous type
collapsed:: true
- ((648c2c54-b536-40ba-8191-ef1aeb2be0b9))
- ((648c2c9a-fcca-43e3-94a6-466f52131b48))
- ((648c2d05-82d4-472f-901c-b362852e2a3a))
- 换元的示例
collapsed:: true
- ((648c2de1-d9a7-4760-bb4f-beec4b41102c))
-
- ((648c488f-85fa-4203-8092-07176b38fce9))
- 公式法 #flashcard
collapsed:: true
- ((648c48ac-76be-4848-af0d-1532467c8d68))
- Mathematical Expectation and Variance ![section 2.3.pdf](../assets/section_2.3_1686916498071_0.pdf)
- Expectation
- Definitions :-> ((648c4e9e-5515-4da3-bc6b-39d6969f5f14))
- Examples:
collapsed:: true
- ((648c5298-fb84-4e9c-b816-7df1a7ad9a66)) #flashcard
collapsed:: true
- ((648c52d9-ea03-4835-8080-52ba5e6c3122))
- Expectation of compound **functions**: (Expectation of Functions of a Random Variable) (Replace $$x$$ with $$g(x)$$) #flashcard
collapsed:: true
- ((648c5381-49cd-4701-ba48-31c0e21474a7))
- Properties:
collapsed:: true
- ((648c568e-c617-4699-b217-fd4e8ea205bc))
- Linerarity:
((648c569c-e3d0-445d-acf6-caf0e271f7be))
- Variance
- Definition:
- ((648c57b6-225a-4926-9ce1-8d0e7aae1391))
-
-
- LATER 学积分
:LOGBOOK:
CLOCK: [2023-06-03 Sat 17:05:07]--[2023-06-03 Sat 17:05:08] => 00:00:01
CLOCK: [2023-06-03 Sat 21:07:06]--[2023-06-03 Sat 21:07:07] => 00:00:01
CLOCK: [2023-06-03 Sat 21:07:17]--[2023-06-03 Sat 21:07:18] => 00:00:01
:END:
- LATER Binomial coefficient
- LATER 写题（作业，对答案）
- LATER 总复习, 考试6.19，杰克6.8
- LATER 看完网课和串讲 [[Jun 17th, 2023]]

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logseq/bak/pages/总复习2023t1/2023-06-16T10_40_41.427Z.android.md → logseq/bak/pages/总复习2023t1/2023-06-16T12_39_58.149Z.android.md
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@ -1309,7 +1309,8 @@
- DONE past year exercise 1
- DONE past year exercise 2
- LATER past year exercise 3
- LATER [[产品开发]] {{renderer :todomaster}}
- DONE [[产品开发]] {{renderer :todomaster}}
collapsed:: true
SCHEDULED: <2023-06-16 Fri>
- ## 往年题考点
- ### Prototypes (2019) Topic 12-13
@ -2601,8 +2602,160 @@
- process to take
- requirements to meet
- LATER 概率论 (隔了一个周末)
collapsed:: true
SCHEDULED: <2023-06-19 Mon>
- {{embed ((647bf024-41f1-45e7-afaf-f49026e826d6))}}
- LATER 概率论 {{renderer :todomaster}}
id:: 647bf024-41f1-45e7-afaf-f49026e826d6
:LOGBOOK:
CLOCK: [2023-06-03 Sat 16:47:39]--[2023-06-03 Sat 16:47:40] => 00:00:01
:END:
- LATER Mind map
deck:: 2023t1/math
collapsed:: true
:LOGBOOK:
CLOCK: [2023-06-16 Fri 15:00:23]--[2023-06-16 Fri 15:18:37] => 00:18:14
:END:
- DONE Ch1
collapsed:: true
:LOGBOOK:
CLOCK: [2023-06-16 Fri 15:31:10]--[2023-06-16 Fri 17:15:08] => 01:43:58
:END:
- Experiment, Sample Space and Random Event ![section 1.2.pdf](../assets/section_1.2_1686899993390_0.pdf)
- Events as Sets
- Definition of Classical Probability, Geometric Probability and Frequency ![section 1.3.pdf](../assets/section_1.3_1686900041785_0.pdf)
collapsed:: true
- **Classical** if
- 1. E contains **only different limited basic** events, that is,
$$ Ω = \{ω1 , ω2 , · · · , ωn \}. $$
We call this kind of sample space simple space, and
2. all outcomes are equally likely to occur.
- **Geometric** if
- (i) the sample space is a **measurable** (such as length, area,
volume, etc.) region, i.e., $$0 < L(Ω) < ∞$$, and
- (ii) the probability of every event $$A ⊂ Ω$$ is proportional to the
measure $$L(A)$$ and has nothing to do with its position and
shape.
- The **Frequency** Interpretation of Probability
- Let E be an random experiment, A be an random event.
Suppose that E was repeated n times under similar conditions.
Let fn (A) be the times that A occurs. The ration
$$Fn (A) =
\frac{ fn (A)}{n}$$
is said to be the frequency of event A in the n trials. If n is
large enough, the probability of event A will be approximated
by Fn (A).
- Problems of Each Interpretation of Probability
- Similarity of the Above Interpretations of probability
- For classical random experiment E, the probability has the fol-
lowing properties:
(i) for every event A, P (A) ⩾ 0,
(ii) P (Ω) = 1,
(iii) for every finite sequence of n disjoint events A1 , A2 , · · · , An ,
![image.png](../assets/image_1686901196592_0.png)
- Property (iii) is called finite additivity.
- Axiomatic Definition of Probability ![section 1.4.pdf](../assets/section_1.4_1686901294123_0.pdf)
- Let P (A)(A ∈ F ) be a non-negative set function on the σ-algebra
F . P (A) is called the probability measure or probability of
event A if it satisfies the following three axioms:
Axiom 1. for every A ∈ F , P (A) ⩾ 0;
Axiom 2. P (Ω) = 1;
Axiom 3. (countable additivity) for every infinite sequence of
countable disjoint events A1 , A2 , · · · ,
![image.png](../assets/image_1686901606535_0.png){:height 185, :width 405}
The sets in σ-algebra F are called events. F is called to be the
algebra of events. ==The triple (Ω, F , P ) is a probability space
or probability triple.==
- Properties of Probability
- $$P (∅) = 0.$$
- For every finite $$A1 , A2 , · · · , An$$,
![image.png](../assets/image_1686901672954_0.png)
- For every event A, $$P (A) = 1 − P (A)$$.
- If A ⊂ B, then P (B − A) = P (B) − P (A) and P (A) ⩽ P (B).
- ==For every two events A and B,==
$$P (A ∪ B) = P (A) + P (B) − P (AB)$$
- ![image.png](../assets/image_1686901846112_0.png)
- The ((648c1a97-e67b-471b-b07f-ae24970d60f6)) of Conditional Probability ![section 1.5.pdf](../assets/section_1.5_1686903326304_0.pdf)
- ![Screenshot from 2023-06-16 16-17-56.png](../assets/Screenshot_from_2023-06-16_16-17-56_1686903487884_0.png)
- ((648c1afb-77a7-4f91-b6e9-20351b320254))
- ((648c1b5f-f72c-495e-8c8a-b184c8682d74))
- ((648c1bb4-f300-43f1-a55f-ca859720ee6b))
- ((648c1e25-4336-48ba-bd20-d156a4c8df7a)) ![section 1.6.pdf](../assets/section_1.6_1686904326481_0.pdf)
- ((648c1e7c-ce3f-4aea-bff6-4d35373becbb))
- ((648c1ea8-997d-4d93-b7ac-c7a5b9300bed))
- Pairwise independence $$\neq$$ Mutually independence
- ((648c2162-314d-4d4b-a3f6-29e39fdcc83b))
- ((648c206e-8ce7-4a74-9ba5-4991d761909f))
- ((648c27ed-e09d-4f1a-8100-7ae2dfff1c8e))
- ((648c27f9-f944-4bf8-9e44-cb3e9048d286))
-
- NOW Ch2 Random Variable
:LOGBOOK:
CLOCK: [2023-06-16 Fri 17:15:12]
:END:
- The Definition of a Random Variable ![section 2.1.pdf](../assets/section_2.1_1686906920851_0.pdf)
- ((648c2860-5454-45f1-80f8-1c85bce84fd1))
- ((648c290a-3532-4e56-8536-258daf7b00a7))
- Distribution Function
- ((648c2970-9091-4f46-8745-b0c10cdeb832))
collapsed:: true
- ((648c2994-36eb-44bf-8038-e49d2390a5b0))
- ((648c2a73-3961-4723-90e8-5f160bb18e0d)) ![section 2.2.pdf](../assets/section_2.2_1686907456219_0.pdf)
collapsed:: true
- ((648c2a88-3d0f-47d2-be44-21df002a1def))
- ((648c2abf-5c5e-4af9-9e13-bb566f3206e8))
- ((648c2b26-e92d-43f7-b8e1-60b51a2b5268))
- Discrete type
collapsed:: true
- Definition: ((648c2be0-787e-4e1f-8d0c-b859f0d08383))
- Continuous type
collapsed:: true
- ((648c2c54-b536-40ba-8191-ef1aeb2be0b9))
- ((648c2c9a-fcca-43e3-94a6-466f52131b48))
- ((648c2d05-82d4-472f-901c-b362852e2a3a))
- 换元的示例
collapsed:: true
- ((648c2de1-d9a7-4760-bb4f-beec4b41102c))
- ((648c488f-85fa-4203-8092-07176b38fce9))
- 公式法 #flashcard
collapsed:: true
- ((648c48ac-76be-4848-af0d-1532467c8d68))
- Mathematical Expectation and Variance ![section 2.3.pdf](../assets/section_2.3_1686916498071_0.pdf)
- Expectation
- Definitions :-> ((648c4e9e-5515-4da3-bc6b-39d6969f5f14))
- Examples:
collapsed:: true
- ((648c5298-fb84-4e9c-b816-7df1a7ad9a66)) #flashcard
collapsed:: true
- ((648c52d9-ea03-4835-8080-52ba5e6c3122))
- Expectation of compound **functions**: (Expectation of Functions of a Random Variable) (Replace $$x$$ with $$g(x)$$) #flashcard
collapsed:: true
- ((648c5381-49cd-4701-ba48-31c0e21474a7))
- Properties:
collapsed:: true
- ((648c568e-c617-4699-b217-fd4e8ea205bc))
- Linerarity:
((648c569c-e3d0-445d-acf6-caf0e271f7be))
- Variance
- Definition:
- ((648c57b6-225a-4926-9ce1-8d0e7aae1391))
-
-
- LATER 学积分
:LOGBOOK:
CLOCK: [2023-06-03 Sat 17:05:07]--[2023-06-03 Sat 17:05:08] => 00:00:01
CLOCK: [2023-06-03 Sat 21:07:06]--[2023-06-03 Sat 21:07:07] => 00:00:01
CLOCK: [2023-06-03 Sat 21:07:17]--[2023-06-03 Sat 21:07:18] => 00:00:01
:END:
- LATER Binomial coefficient
- LATER 写题（作业，对答案）
- LATER 总复习, 考试6.19，杰克6.8
- LATER 看完网课和串讲 [[Jun 17th, 2023]]
:LOGBOOK:
CLOCK: [2023-06-16 Fri 14:42:58]--[2023-06-16 Fri 14:55:49] => 00:12:51
:END:
- [6-8](https://meeting.tencent.com/user-center/shared-record-info?id=7bb557da-b99f-4316-ab5e-fe96befe28b0&from=3)
- LATER 写思维导图
- [[Jun 16th, 2023]]: Ch 1 - 3
- [[Jun 17th, 2023]]: Ch 6-8
- LATER 做题 [[Jun 18th, 2023]]
- ![2023-06-09-13-21-19.jpeg](../assets/2023-06-09-13-21-19.jpeg)
-

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@ -61,4 +61,11 @@ file-path:: ../assets/section_2.3_1686916498071_0.pdf
hl-color:: yellow
id:: 648c57e8-e79a-48b6-98cf-f68dc0e5277e
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hl-stamp:: 1686919143722
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hl-page:: 32
hl-color:: yellow
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hl-type:: area
hl-stamp:: 1686919183374

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@ -2738,9 +2738,10 @@
- Definition:
- ((648c57b6-225a-4926-9ce1-8d0e7aae1391))
- Alternative calculation:
-
- ((648c580f-8ccb-4fd3-bc0d-24ab109f240d))
- ((648c57d7-8f76-4520-8bc0-b54953bbe4cf))
- Standard variance: ((648c57e8-e79a-48b6-98cf-f68dc0e5277e))
-
- LATER 学积分
:LOGBOOK:
CLOCK: [2023-06-03 Sat 17:05:07]--[2023-06-03 Sat 17:05:08] => 00:00:01