Harvard statistics 110, video 1 note(probability & counting)

8:58 2014-10-01 Wednesday
start Harvard statistics 110, video I


probability & counting


8:59 2014-10-01
to improve your pattern recognition skills


9:00 2014-10-01
pattern recognition


9:00 2014-10-01
some of you may be rusty on your math


9:07 2014-10-01
story proof


9:07 2014-10-01
strategic practice


9:07 2014-10-01
naive definition of probability, which is 


kind of historical roots of the subject


9:09 2014-10-01
quickly move beyond the naive stage


9:09 2014-10-01
gambling is where statistics come from,


the historical roots 


9:16 2014-10-01
game of chance


9:16 2014-10-01
dice, cards, coins


9:16 2014-10-01
standard deck of cards


9:16 2014-10-01
math is the logic of certainty;


statistics is the logic of uncertainty.


9:20 2014-10-01
it' going to be about quantifying uncertainty.


9:20 2014-10-01
naive definition of the probability.


9:21 2014-10-01
sample space


9:21 2014-10-01
experiment


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outcome


9:21 2014-10-01
A sample space is the set of all possible outcomes


of an experiment.


9:22 2014-10-01
An event is a subset of a sample space.


9:23 2014-10-01
the idea of using set.


9:23 2014-10-01
we're going to do some deeply deeply contraintuitive


thing to almost anyone.


9:27 2014-10-01
lot of paradox, lot of surprise makes statistics


more fun than calculus.


9:27 2014-10-01
the breakthough: think events as subsets.


9:28 2014-10-01
naive definition of prabability:


P(A) = #favorable outcomes / #possible outcomes


9:30 2014-10-01
flip a coin twice: 


HH, HT, TT, TH // all possibe outcomes


9:33 2014-10-01
fair coin: heads & tails are equally likely


9:34 2014-10-01
we treat them all as equally likely


9:34 2014-10-01
they use naive definition without justification.


9:37 2014-10-01
we'll need to be quickly beyond this.


9:38 2014-10-01
some basic principle of counting:


* multiplication rule


9:40 2014-10-01
combined experiment


9:43 2014-10-01
tree diagram


9:43 2014-10-01
ice cream example:


1. which type of cone you want?


2. which type of flavor you want?  // chocolate, vanilla, strawberry


9:44 2014-10-01
you can draw this tree diagram yourself.


9:47 2014-10-01
you all know exponential growth.


9:47 2014-10-01
grow exponentially fast.


9:48 2014-10-01
Binomial coefficient: choose k from n


9:50 2014-10-01
choose a subset of size k, where order doesn't matter


9:51 2014-10-01
order matters         // permutation


order does not matter // combination


10:01 2014-10-01
there is a couple of loose ends