Module Three: Anticipating Patterns


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  Probability:

  • Interpreting probability, including long-run relative frequency interpretation
  • 'Law of Large Numbers' concept
  • Addition rule, multiplication rule, conditional probability, and independence
  • Discrete random variables and their probability distributions, including binomial and geometric
  • Simulation of random behavior and probability distributions
  • Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable

  Combining independent random variables:

  • Notion of independence versus dependence
  • Mean and standard deviation for sums and differences of independent random variables

  The Normal distribution:

  • Properties of the Normal distribution
  • Using tables of the Normal distribution
  • The Normal distribution as a model for measurements

Sampling distributions:

  • Sampling distribution of a sample proportion
  • Sampling distribution of a sample mean
  • Central Limit Theorem
  • Sampling distribution of a difference between two independent sample proportions
  • Sampling distribution of a difference between two independent sample means
  • Simulation of sampling distributions
  • t-distribution
  • Chi-square distribution

  Probability:

  • Interpreting probability, including long-run relative frequency interpretation
  • 'Law of Large Numbers' concept
  • Addition rule, multiplication rule, conditional probability, and independence
  • Discrete random variables and their probability distributions, including binomial and geometric
  • Simulation of random behavior and probability distributions
  • Mean (expected value) and standard deviation of a random variable and linear transformation of a random variable

  Combining independent random variables:

  • Notion of independence versus dependence
  • Mean and standard deviation for sums and differences of independent random variables

  The Normal distribution:

  • Properties of the Normal distribution
  • Using tables of the Normal distribution
  • The Normal distribution as a model for measurements

Sampling distributions:

  • Sampling distribution of a sample proportion
  • Sampling distribution of a sample mean
  • Central Limit Theorem
  • Sampling distribution of a difference between two independent sample proportions
  • Sampling distribution of a difference between two independent sample means
  • Simulation of sampling distributions
  • t-distribution
  • Chi-square distribution

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