Stat 88

Probability and Mathematical Statistics for Data Science

Question: which of my following of my intended degrees do you think statistics is a requirement for?  Mechanical Engineering major, Business major, or EECS minor?  If you guessed one of my STEM degrees, you are incorrect despite your sound logic.  Statistics is a math class >> math is a STEM field >> must be one of your STEM majors.  Sorry, but it was actually my Business major!  I am pleasantly surprised by Berkeley’s decision to make a statistics class a core prerequisite for upper division business courses.  In fact, if I had not been blessed with the opportunity to pursue a dual major (in contrast to a singular engineering major that would have been my second option), I would never have taken statistics as it is ironically NOT required for Engineering.  This would have been a Shakespearean tragedy of a missed opportunity.  

Rewind to my junior year in high school. My chemistry teacher casually drops during class that everyone, regardless of major or career choice, should take statistics.  Prior to then, I had no intention of ever taking a statistics course, much less learning the basics on my own.  Though I had the option to take statistics my senior year, I chose the calculus course which I believed would be “more rigorous” and “look better to colleges”.  

Enter UC Berkeley.  Throughout my freshman year, I still had no intention to heed the wise words of my chemistry teacher and was fully prepared to live a statistics-less life.  Eventually, Stat 88 finds its way into my schedule.  I did not blink when enrolling.  The course was merely part of the due process of receiving my major.  My attitude was: “let’s get this over with shall we?”.  Since then, my perspective on statistics changed quite a bit. 

As with many of these basic courses that are similarly taught at all colleges and/or high schools, I will briefly gloss over the material.  Stat 88 is split into two distinct halves.  Pre-midterm 1, the class focused on teaching the basics of probability and the arsenal of common distributions such as the binomial, hypergeometric, and Poisson distributions.  The second half of the course placed emphasis on applications of distributions, their means, and variances as well as dabbled into data science topics such as confidence intervals and linear regression.  

Common distributions and their relationships. Not all of these distributions were covered in Stat 88.

I can only describe the learning of the different distributions as a series of epiphanies.  One after another, each distribution helped tackle previously challenging probability problems and narrowed them down to a strict and straightforward science.  Each distribution had me scratching my head at the outset and uttering a prolonged mental “ohhhhhh” after picking apart and understanding the “why”.  

If learning the basic distributions were a series of “ohhhh”s, then learning the applications of means and variances as well as their applications to large datasets were a series of “hot damn that is useful”s.  Difficult, yet intriguing, the problems motivated me to fully understand the material solely out of how practical they seemed.  I mean you tell me to find the inverse of a matrix and I’m saying “what the hell am I doing this for?”.  Then you tell me to determine “whether a vaccine is statistically effective” and I’m all for it.  

In closing, this is the class I never knew I needed.  And if you have never taken the subject, change that.  I now concur with my chemistry teacher.  I guess he does know what he’s talking about.  He went to Yale after all.  

Food For Thought

One interesting and simple way to make a coin biased is to simply bend it! Devise a plan to simulate a fair coin toss when you only have one bent coin in your pocket.

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