Harvard Fat Chance: probability from ground up
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most novel contribution of this course
intuitive introduction to counting with many examples
interesting counting problems and puzzles explained with counting and probability concepts
illuminating introduction to normal distribution and central limit theorem
Introduction
Keywords
statistics, probability, counting, language, practice, high school math
Counting
Keywords
counting, rule 1 and rule 2 derived from finger with transformation
counting practices
counting even numbers
Large numbers
Keywords
large numbers, exponential notations, scientific notations
Multiplication rule
Keywords
multiplication rule
More multiplication rule
Keywords
multiplication rule with factorial
The subtraction principle
Keywords
subtraction rule with more complex practices
Counting Collection
keywords
sequences, collections
Application of Collection
keywords
how sequence counting and collection counting work together
Binomial coefficient
keywords
binomial theorem, pascal triangle
multinomials and practice
keywords
how to count ways for n object splitting into two or more groups
Collection with repetition
keywords
how to do collection count while allow repetition
coin flipping with intro to probability
keywords
move from counting to probability or ratio
rolling die
key questions
How to understand probabilities behind rolling die
poker probability
key questions
how to understand probabilities behind poker
Bridge hands and birthday paradox
key questions
How much wrong our intuition or common sense expectation can be in the light of dealing cards and birthday paradox problem?
Expectation
key questions
how to understand expectation in gambling games
Expected value slot machine
key questions
relation between outcome, payoff and probability
how to understand the probability behind slot machine
Expected Value Strategizing
key questions
Expectation can help decisions but with many constraints
how to compare many games for the best one using Expectation?
The Monty Hall problem
Key questions
how to understand Monty Hall problem with conditional probability?
Conditional probability setup and examples
key questions
to understand conditional probability with total probability of sum
Conditional probability with election
key questions
How to understand and use bayes rule?
Bernoulli trials
key questions
how to understand bernoulli trials from flipping coins examples
Gambler's ruin
key questions
what if we don't know how many trials to do, then we can't use bernoulli or binomial trials
how to find out the probability of winning, only given p(win), a(initial capital), b(capital goal), a down to 0 = end game
Games
key questions
how to calc expectation value and variance
properties of ev(G + c), ev(G x d), var(G+c), var(G x d)
Example and variance
key questions
how to calc variance (not very illuminating)
The iterating game
key questions
how to calc prob of flipping coin large number of times
quick formula for calc G(n)'s mean and variance
The normal distribution
key questions
the practical purpose of normal distribution from coin flipping view
why we need standard normal distribution or bell curve
Interesting point
large number of averages: chance of getting 600 or more heads of 1000 flips is much much less than chance of getting 60 heads from 100 flips
practice
a very comprehensive problem solution to use normal dist to calc 520 heads or more from coin flipping 1000
The normal distribution part 2
video links
Key questions
how to calc probability between two payoff values?
intuitive introduction to central limit theorem
- extend normal distribution to calc probability of large iterations of any game
practice
very comprehensive problem solution to exten normal distribution to huge number of iterations of any game
how to use Z-table