12 Concepts That Change How You See Probability Distributions

There are many ways to describe a random variable (i.e., probability distribution). Some of these are fairly well known, such as the mean and variance of a distribution. Others are less so, such as skewness or kurtosis.

This video tries to synthesize 12 key concepts underlying the ways we describe random variables in just 10 minutes! This includes:

The central tendency of a distribution (median, mode, and mean)
Dispersion measures (variance, standard deviation, coefficient of variation)
Skewness and kurtosis to understand the distribution tails
An explanation of moments (raw, central, standardized) and how a core concept in physics is the basis of our descriptors in probability and statistics.

0:00 Introduction
1:01 Mode
1:31 Median
1:50 Raw Moments in Probability
2:50 Mean
3:26 Central Moments in Probability
3:43 Dispersion Measures: Variance, Standard Deviation, Coefficient of Variation
5:02 Standardized Random Variables
6:16 Standardized Moments in Probability
6:23 Skewness
8:24 Kurtosis
9:59 Conclusion

#probability #statistics #datascience #mean #variance #kurtosis #skewness #mathematics #education

Side Note: In the video, I comment that the moments in probability 'likely' come from physics. In reality, this relationship is quite strong (and goes back quite a bit in time). For example, this relationship is fairly clear in Karl Pearson's 1893 note "Asymmetrical Frequency Curves" with his discussion of the binomial distribution. In fact, he starts this note by stating, "...curves occurring in physical and biological measurements."

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May 2, 2025: Thanks to all past viewers and followers of this channel for your patience! We just had a kid, which impacted my ability to produce timely content. I'll be spending the next few months building out the blog I initially created last year (riskbynumbers.org and riskbynumbers.com). Definitely feel free to provide comments or feedback around the type of content you'd like to learn more about by commenting on this video or reaching out to me directly.

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If this is your first video, welcome! I am a professor sharing educational resources around probability, statistics, optimization methods, algorithms, and programming to a broad audience.

Outside of YouTube, you can currently find me in Vancouver, Canada at the University of British Columbia.

Thank you, and I look forward to seeing you in future videos!

Email: RiskByNumbers@gmail.com.
LinkedIn:   / omar-swei