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Probability

5.7 Limit Theorems

Joshua Fan

Alex Tsun

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Agenda

  • The Sample Mean
  • The Law of Large Numbers (LLN)
  • The Central Limit Theorem (CLT)
  • The Continuity Correction

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Sample Mean

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The Law of Large Numbers

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The Law of Large Numbers

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The Law of Large Numbers

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The Central Limit Theorem

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The Central Limit Theorem

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The Central Limit Theorem

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The Central Limit Theorem

Proved Using MGFs! (future video)

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Random Picture

Definition of

Expectation

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CLT (Pictures)

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CLT (Pictures)

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CLT (Pictures)

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CLT (Pictures)

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CLT (Pictures)

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CLT (Pictures)

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CLT (Pictures)

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CLT (Pictures)

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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CLT (Example)

Definition of

Expectation

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The Continuity Correction (Idea)

Definition of

Expectation

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The Continuity Correction (Idea)

Definition of

Expectation

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The Continuity Correction (Idea)

Definition of

Expectation

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The Continuity Correction (Idea)

Definition of

Expectation

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The Continuity Correction (Idea)

Definition of

Expectation

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The Continuity Correction

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The Continuity Correction

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END PIC

Alex Tsun

Joshua Fan