Introduction

Statistics

variance and standard deviation = dispersion (集中 or 分散)

expected value = 長期平均獲利

covariance = two variables have same changes or not

	Example One	Example Two
	-10, 0, 10, 20, 30	8, 9, 10, 11, 12
mean (average)	(-10 + 0 + 10 + 20 + 30) / 5 = 10	(8 + 9 + 10 + 11 + 12) / 5 =10
variance	200	2
standard deviation	141	1.41

Expected value

1. the long-run average value of the same experiment

2. Whole population mean

E(x) = sum(probability * x_value)

打擊率0.35的選手打100球, 期望打到35球

Convairance

1. stock A & stock B move at the same direction -> positive covariance

2. stock A & stock B move at the opposite direction -> negative covariance

3. Covariance =(1) how far the variables are spread out (2) the nature of their relationship

4. degree to which two variables are linearly associated.

5. Two are independent will have covariance = 0

Correlation is a scaled version of covariance that takes on values in [−1,1]

Binomial / Bernoulli / Poisson

Binomial Distribution

1. discrete probability distribution.

2. Outcome is True or False. (Dice shows 4, or not 4)

Bernoulli distribution

1. two possible outcome

2. For a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution.

Poisson process

1. we know the average time between events but they are randomly spaced (stochastic)

2. Earthquake happens every 5 years in A-zone, but we don't know when is next.

3. the binomial distribution with large trials(continuous) and rare happens = poisson

lambda = expected number of events in the interval

Meteor example

Waiting time

the probability of waiting less than or equal to a time:

wait for 6mins, you will have 39% chance to see a meteor.

1 - math.exp((1/12)*6) = 39%

https://towardsdatascience.com/the-poisson-distribution-and-poisson-process-explained-4e2cb17d459