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@ -152,4 +152,4 @@
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:page 27},
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:page 27},
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:content {:text "[:span]", :image 1686922716232},
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:content {:text "[:span]", :image 1686922716232},
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:properties {:color "yellow"}}],
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:properties {:color "yellow"}}],
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:extra {:page 28}}
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:extra {:page 29}}
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@ -2719,6 +2719,7 @@
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- ((648c2de1-d9a7-4760-bb4f-beec4b41102c))
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- ((648c2de1-d9a7-4760-bb4f-beec4b41102c))
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- ((648c488f-85fa-4203-8092-07176b38fce9))
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- ((648c488f-85fa-4203-8092-07176b38fce9))
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- 公式法 #flashcard
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- 公式法 #flashcard
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id:: 648c4893-5e69-41dc-95a4-090a06cd1735
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collapsed:: true
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collapsed:: true
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- ((648c48ac-76be-4848-af0d-1532467c8d68))
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- ((648c48ac-76be-4848-af0d-1532467c8d68))
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- Mathematical Expectation and Variance ![section 2.3.pdf](../assets/section_2.3_1686916498071_0.pdf)
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- Mathematical Expectation and Variance ![section 2.3.pdf](../assets/section_2.3_1686916498071_0.pdf)
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- Expectation
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- Expectation
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collapsed:: true
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collapsed:: true
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- Definitions :-> ((648c4e9e-5515-4da3-bc6b-39d6969f5f14))
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- Definitions :-> ((648c4e9e-5515-4da3-bc6b-39d6969f5f14))
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id:: 648c4e9f-7b40-4df5-ab81-e6eb49536831
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- Examples:
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- Examples:
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collapsed:: true
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collapsed:: true
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- ((648c5298-fb84-4e9c-b816-7df1a7ad9a66)) #flashcard
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- ((648c5298-fb84-4e9c-b816-7df1a7ad9a66)) #flashcard
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id:: 648c52b8-5174-4dfc-8954-d58b27893865
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collapsed:: true
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collapsed:: true
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- ((648c52d9-ea03-4835-8080-52ba5e6c3122))
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- ((648c52d9-ea03-4835-8080-52ba5e6c3122))
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- Expectation of compound **functions**: (Expectation of Functions of a Random Variable) (Replace $$x$$ with $$g(x)$$) #flashcard
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- Expectation of compound **functions**: (Expectation of Functions of a Random Variable) (Replace $$x$$ with $$g(x)$$) #flashcard
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id:: 648c52dc-1cfe-4c05-888a-d8ddff10c24e
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collapsed:: true
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collapsed:: true
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- ((648c5381-49cd-4701-ba48-31c0e21474a7))
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- ((648c5381-49cd-4701-ba48-31c0e21474a7))
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- Properties:
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- Properties:
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- Examples
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- Examples
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collapsed:: true
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collapsed:: true
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- ((648c5b1c-533d-434a-b118-6a61cc9abb3a)) #flashcard
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- ((648c5b1c-533d-434a-b118-6a61cc9abb3a)) #flashcard
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id:: 648c5ae4-9e42-4c55-86d0-b0a19dfcb4dc
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collapsed:: true
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collapsed:: true
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- ((648c5b30-e75f-4f0c-bb7d-985442728fbe))
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- ((648c5b30-e75f-4f0c-bb7d-985442728fbe))
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- LATER Moments of random variable
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- LATER Moments of random variable
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collapsed:: true
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collapsed:: true
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- Definition :-> ((648c5c3a-160a-41ff-9cc7-83e750e3e8fa))
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- Definition :-> ((648c5c3a-160a-41ff-9cc7-83e750e3e8fa))
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id:: 648c5c30-6a99-41f4-be4c-e5e22387647a
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- Application of Expectation and Variation
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- Application of Expectation and Variation
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collapsed:: true
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collapsed:: true
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- *Markov's inequality*: when **only mean** is known #flashcard
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- *Markov's inequality*: when **only mean** is known #flashcard
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id:: 648c5c5c-623c-43de-b750-b997db48e6dd
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collapsed:: true
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collapsed:: true
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- ((648c5c6f-d6b4-4c65-b9a4-9f51f93f86ad))
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- ((648c5c6f-d6b4-4c65-b9a4-9f51f93f86ad))
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- *Chebyshev's inequality*: when **mean an variance are** known #flashcard
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- *Chebyshev's inequality*: when **mean an variance are** known #flashcard
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id:: 648c5c71-3ec9-47db-8433-e1325b3a8c20
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collapsed:: true
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collapsed:: true
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- ((648c5c81-d93b-4859-9ee0-37cceb8fd100))
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- ((648c5c81-d93b-4859-9ee0-37cceb8fd100))
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- **Usage** of Markov's inequality and Chebyshev's inequality
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- **Usage** of Markov's inequality and Chebyshev's inequality
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- ((648c5e0c-b0b1-4129-b172-3ff95ff4a41c)) and ((648c5e26-8a90-4db2-919f-356a164e5a2b)) ![section 2.4.pdf](../assets/section_2.4_1686920705980_0.pdf)
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- ((648c5e0c-b0b1-4129-b172-3ff95ff4a41c)) and ((648c5e26-8a90-4db2-919f-356a164e5a2b)) ![section 2.4.pdf](../assets/section_2.4_1686920705980_0.pdf)
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- Binomial Distribution
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- Binomial Distribution
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- Definition: #flashcard
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- Definition: #flashcard
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id:: 648c5ef0-fd5e-4f17-9e2d-fde0c67e53c6
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- ((648c5fc2-c838-473b-9b29-f238ae3a96ca))
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- ((648c5fc2-c838-473b-9b29-f238ae3a96ca))
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- ((648c5f9a-646f-4eea-9d03-597d8598f752))
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- ((648c5f9a-646f-4eea-9d03-597d8598f752))
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- ((648c5fa8-25a4-47ba-a285-e9399f719543))
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- ((648c5fa8-25a4-47ba-a285-e9399f719543))
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- Properties:
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- Properties:
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- mean, variance :-> ((648c6007-c181-4e85-9a88-046841e6739d))
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- mean, variance :-> ((648c6007-c181-4e85-9a88-046841e6739d))
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id:: 648c6001-da22-465c-95f1-51a7e5292cb3
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- Examples:
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- Examples:
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collapsed:: true
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collapsed:: true
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- ((648c62d4-454b-43ab-88a8-d35a5a867523))
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- ((648c62d4-454b-43ab-88a8-d35a5a867523))
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- ((648c63b8-21ff-42d4-ad87-70c706124ba1))
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- ((648c63b8-21ff-42d4-ad87-70c706124ba1))
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- LATER Poisson limit theorem #flashcard (when n is infinity, this become Poisson distribution)
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- LATER Poisson limit theorem #flashcard (when n is infinity, this become Poisson distribution)
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id:: 648c63bc-2465-42e5-833f-abd152201631
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- ((648c63da-deea-42ab-8f72-f3219d4fecbc))
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- ((648c63da-deea-42ab-8f72-f3219d4fecbc))
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- Poisson distribution
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- Poisson distribution
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- Definition: :-> ((648c653d-ed40-4938-9124-cf4c2c296867))
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- Definition: :-> ((648c653d-ed40-4938-9124-cf4c2c296867))
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id:: 648c6510-49a0-4673-bf16-4cf9f47efa14
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- Use cases:
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- Use cases:
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collapsed:: true
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collapsed:: true
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- ((648c65ba-0f8f-4371-a52e-e78e8b3ae512))
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- ((648c65ba-0f8f-4371-a52e-e78e8b3ae512))
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- Properties:
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- Properties:
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- Variance, mean :-> ((648c65dd-356b-4209-85ae-e881033fcea8))
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- Variance, mean :-> ((648c65dd-356b-4209-85ae-e881033fcea8))
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id:: 648c65d1-7592-43f7-a12c-d96d9e76a492
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- LATER 学积分
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- LATER 学积分
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:LOGBOOK:
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:LOGBOOK:
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CLOCK: [2023-06-03 Sat 17:05:07]--[2023-06-03 Sat 17:05:08] => 00:00:01
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CLOCK: [2023-06-03 Sat 17:05:07]--[2023-06-03 Sat 17:05:08] => 00:00:01
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