P4-1 Central Limit Theorem - part 1/3 (Formal definition)

The Central Limit Theorem states that sums and averages of independent and identically distributed random variables from any distribution have an approximate normal distribution for sufficient large sample sizes. This video provides a few real world examples that demonstrate this phenomenon. Then the video provides the formal definition for this Central Limit Theorem.

Central Limit Theorem: part 2: https://youtu.be/Q11BS_wnq3w part 3: https://youtu.be/uX1UOP09JuA

STAT 587: https://www.jarad.me/courses/stat587Eng/ Slides: https://www.jarad.me/courses/stat587Eng/slides/Probability/P4-Central_limit_theorem/P4-Central_Limit_Theorem.pdf

01:18 - Bell-shaped curve 02:34 - Histograms of 1,000 normal random variables 03:31 - Yield histogram 03:59 - SAT score histogram 04:49 - Histograms of 20 normal random variables 05:22 - Tensile strength histograms 06:16 - Sums and averages of iid random variables 09:08 - Central Limit Theorem

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