HARVARD FILMED THE FIRST LECTURE OF THEIR MOST POPULAR STATISTICS COURSE - TAUGHT BY A PROFESSOR WHOSE STUDENTS CALL HIM THE BEST TEACHER THEY HAVE EVER HAD - AND IT PROVES WHY EVEN ISAAC NEWTON GOT PROBABILITY WRONG
This is Joe Blitzstein, Harvard, Statistics 110, lecture 1. He has won Harvard's Excellence in Teaching award multiple times, his textbook Introduction to Probability is used in over 200 universities worldwide, and his online course has been taken by over 2 million people across 190 countries. He opens by saying that after a few weeks of this course you will easily solve calculations that 300 years ago required consulting Isaac Newton - and Newton's intuition was still wrong.
He traces probability to Fermat and Pascal writing letters back and forth in the 1650s analyzing gambling games. No one had mathematically derived the rules before. They invented the subject by betting on dice in correspondence. Then he shows why the naive definition - probability equals favorable outcomes divided by total outcomes - breaks immediately. Ask what the probability of life on Neptune is. Either there is or there isn't. By the naive definition the answer is 1/2. So is the probability of intelligent life on Neptune. Something is severely wrong.
Then the multiplication rule. Two types of ice cream cone and three flavors gives 6 combinations - not because you memorized it but because you can draw a tree and count branches. Every counting problem in the course is just a bigger version of that tree. Then binomial coefficients - n choose k counts the number of ways to select k objects from n when order doesn't matter. The full house in poker falls out in 4 lines of multiplication once you understand the tree.
Watch the moment he fills in the sampling table - with or without replacement, order matters or doesn't. Three of the four boxes are immediate from the multiplication rule. The fourth requires a proof he saves for next lecture. That one box is harder than the other three combined.
A data scientist I know rewatched this lecture before switching careers into statistics. Said it was the first time probability felt like a system with rules rather than a collection of tricks.
Free on YouTube, Harvard, over 2 million views.
bookmark this and watch later - after this lecture you will never again confuse equally likely with obviously true
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Nvidia CEO Jensen Huang just made the boldest prediction of his career:
“AI will create more millionaires in 5 years than the internet did in 20.”
But he didn’t stop there.
He revealed exactly HOW it’ll happen
Here’s his framework for capitalizing before it’s too late: ⬇️
The S&P 500 is up 26% the past three months, one of the greatest three month returns ever.
On the surface this might sound like weakness is coming, but that isn't necessarily true. Never lower 3, 6, and 12 months later with above avg returns across the board as well.
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S&P 500 in the 30 years ending 2023:
+10.1% annual return
Finished up 80% of all years
Down double digits 4 of the years
Up double digits 19x
4 out of every 10 years finished up 20% or more
Not bad considering everything that transpired
https://t.co/hTPR1buRGY