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

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本文介绍了哈佛大学统计110课程中的概率与计数基础知识，包括样本空间、事件定义及概率的基本计算方法。通过硬币翻转等实例，讲解了如何使用朴素的概率定义来解决简单的问题，并探讨了组合实验中可能结果的数量计算。

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