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Section 12: Convergence and the Central Limit Theorem

Instructions

  • This section covers the concepts listed below. 
  • For each concept, there is a conceptual video explaining it followed by videos working through examples. 
  • This is the last section so you should return to the main Mathematical Probability page when you finish the material.
Strong Law of Large Numbers and Almost Sure Convergence

Examples


Directions: There are no video examples for this topic.
 

Self-Assessment Questions


Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
  1. Explain almost sure convergence of a sequence of random variables.
  2. What does the Strong Law of Large Numbers claim?
Convergence in Distribution

Examples


Directions: There are no video examples for this topic.
 

Self-Assessment Questions


Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
  1. Explain convergence in distribution and its connection to moment generating functions.
Central Limit Theorem

Examples


Directions: The following examples cover the material from the video above. 
 

Self-Assessment Questions


Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
  1. State the Central Limit Theorem. What is the significance of the Central Limit Theorem?
  2. What does "i.i.d" mean?