Harvard statistics 110, video 1 note(probability & counting)
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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
9:21 2014-10-01
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
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
9:21 2014-10-01
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
0 0
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