Limit Theorems

Limit theorems, Markovs inequality theorem, Chebyshevs inequality theorem, Law of large numbers.

Course Lectures

• Introduction: Probability and Counting

  Mark Sawyer

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  Outcomes, sample, space, events, and probability functions.

• Probability Functions

  Mark Sawyer

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  Probability functions, permuations.

• Permutations

  Mark Sawyer

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  Permutations.

• Probability Functions (continued)

  Mark Sawyer

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  Probability functions.

• Conditional Probability

  Mark Sawyer

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  Conditional probability.

• Conditional Probability (continued)

  Mark Sawyer

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  Conditional probability.

• Independent Events

  Mark Sawyer

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  independence of 3 or more events.

• Random Variables

  Mark Sawyer

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  Random variables.

• Expected Values

  Mark Sawyer

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  Random variables (continued), expected value, standard deviations.

• Binomial Distributions

  Mark Sawyer

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  Standard distribution, binomial distribution, two random variables.

• Midterm Review

  Mark Sawyer

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  Midterm review.

• Multinomial Distributions

  Mark Sawyer

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  Multivariable distribution, binomial distribution, Bernoulli trials, geometric distributions.

• Geometric Distributions

  Mark Sawyer

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  Geometric distributions.

• Poisson Distributions

  Mark Sawyer

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  Poisson distribution, continuous trials, poisson processes.

• Poisson Distributions (continued)

  Mark Sawyer

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  Poisson distribution, poisson processes.

• Density Function

  Mark Sawyer

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  Density funtion, continuous random variables, uniform distribution.

• Exponential Distributions

  Mark Sawyer

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  Continuous random variables, exponential distribution.

• Normal Distributions

  Mark Sawyer

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  Normal distribution.

• Normal Distributions (continued)

  Mark Sawyer

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  Standard normal distribution, cumulative distribution function.

• Standard Normal Distributions

  Mark Sawyer

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  Nomal distribution continued.

• Central Limit Theorem

  Mark Sawyer

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  Central limit theorem, normal distribution applications.

• Hitstogram Correction

  Mark Sawyer

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  Normal approximation, histogram correction.

• Midterm Review 2

  Mark Sawyer

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  Midterm review 2.

• Analyzing Data in Probability

  Mark Sawyer

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  Analyzing data in probability, samples, incomplete data, means.

• Analyzing Data in Probability (continued)

  Mark Sawyer

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  Analyzing data in probability, samples, incomplete data, means.

• Limit Theorems

  Mark Sawyer

  Playing

  Limit theorems, Markovs inequality theorem, Chebyshevs inequality theorem, Law of large numbers.

• Limit Theorems (continued)

  Mark Sawyer

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  Limit theorems, Markovs inequality theorem, Chebyshevs inequality theorem, Law of large numbers.

• Course Review

  Mark Sawyer

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  Course Review