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Probability, Random Variables, and Statistical Inference: Study Notes for Elementary Statistics

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Basic Concepts of Probability

  • Guided course
    Introduction to Probability
    5:37

Complements

  • Guided course
    Complementary Events
    4:23

Addition Rule

  • Guided course
    Probability of Mutually Exclusive Events
    5:14
  • Guided course
    Probability of Non-Mutually Exclusive Events Example
    2:57
  • Guided course
    Probability of Non-Mutually Exclusive Events
    5:14

Multiplication Rule: Independent Events

  • Guided course
    Probability of Multiple Independent Events
    05:54

Multiplication Rule: Dependent Events

  • Guided course
    Conditional Probability Rule Example 1
    03:06
  • Guided course
    Multiplication Rule: Dependent Events
    05:17
  • Guided course
    Conditional Probability Rule
    03:53

Discrete Random Variables

  • Guided course
    Expected Value (Mean) of Random Variables
    04:14
  • Guided course
    Intro to Random Variables & Probability Distributions
    07:09
  • Guided course
    Variance & Standard Deviation of Discrete Random Variables
    04:48

Binomial Distribution

  • Guided course
    Finding Binomial Probabilities Using TI-84 Example 1
    03:33
  • Guided course
    Finding Binomial Probabilities Using TI-84 Example 2
    04:20
  • Guided course
    Mean & Standard Deviation of Binomial Distribution
    03:28

Poisson Distribution

  • Guided course
    Introduction to the Poisson Distribution
    04:00
  • Guided course
    Finding Poisson Probabilities Using TI-84
    03:37
  • Guided course
    Using the Poisson Distribution to Approximate the Binomial Distribution
    04:09

Uniform Distribution

  • Guided course
    Uniform Distribution
    06:06
  • Guided course
    Uniform Distribution Example 1
    02:50

Sampling Distribution of the Sample Mean and Central Limit Theorem

  • Guided course
    Central Limit Theorem Example 1
    02:33
  • Guided course
    Central Limit Theorem
    05:14
  • Guided course
    Sampling Distribution of Sample Mean
    06:53

Introduction to Confidence Intervals

  • Guided course
    Critical Values: z Scores
    04:46
  • Guided course
    Introduction to Confidence Intervals
    06:33

Confidence Intervals for Population Proportion

  • Guided course
    Constructing Confidence Intervals for Proportions Example 1
    06:38
  • Guided course
    Finding the Minimum Sample Size Needed for a Confidence Interval
    04:08
  • Guided course
    Constructing Confidence Intervals for Proportions Example 2
    04:24

Confidence Intervals for Population Mean

  • Guided course
    Finding t-Values Using a TI-84
    05:47
  • Guided course
    Critical Values: t-Distribution
    05:50
  • Guided course
    Finding Confidence Intervals Using TI-84
    04:30

Steps in Hypothesis Testing

  • Guided course
    Step 4: State Conclusion
    09:56
  • Guided course
    Step 2: Calculate Test Statistic
    06:34
  • Guided course
    Step 1: Write Hypotheses
    06:21

Performing Hypothesis Tests: Proportions

  • Guided course
    Performing Hypothesis Tests: Proportions
    05:52
  • Guided course
    Performing Hypothesis Tests: Proportions Example 1
    07:06
  • Guided course
    Performing Hypothesis Tests: Proportions Using TI-84
    03:32

Performing Hypothesis Tests: Means

  • Guided course
    Standard Deviation (σ) Unknown Example 3
    05:55
  • Guided course
    Standard Deviation (σ) Known Example 1
    06:38
  • Guided course
    Standard Deviation (σ) Known
    06:34