Probability and Statistics Course | Khan Academy

[shannon112]

Introduction to Random Variables: https://www.youtube.com/watch?v=IYdiKeQ9xEI
Random variables: https://www.youtube.com/watch?v=3v9w79NhsfI
Discrete and continuous random variables: https://www.youtube.com/watch?v=dOr0NKyD31Q
(like a variable xy but XY, like a function map the random process to a number)
Probability distribution for RA: https://www.youtube.com/watch?v=cqK3uRoPtk0&feature=youtu.be
Probability density functions: https://www.youtube.com/watch?v=Fvi9A_tEmXQ
(在數學中，連續型隨機變量的機率密度函數（在不至於混淆時可以簡稱為密度函數）是一個描述這個隨機變量的輸出值，在某個確定的取值點附近的可能性的函數。圖中，橫軸為隨機變量的取值，縱軸為機率密度函數的值，而隨機變量的取值落在某個區域內的機率為機率密度函數在這個區域上的積分。)

[shannon112]

Binomial Distribution
for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution.
https://en.wikipedia.org/wiki/Binomial_distribution

PMF :

example: X=執五次硬幣正面的次數，p=0.5
example: X=投五次籃進的次數，p=0.3
https://www.youtube.com/watch?v=O12yTz_8EOw
https://www.youtube.com/watch?v=FI8xtVaI068
https://www.youtube.com/watch?v=vKNpQ_KTXvE
https://www.youtube.com/watch?v=H0ZgOGWUcJw

[shannon112]

Normal (or Gaussian or Gauss or Laplace–Gauss) distribution
https://en.wikipedia.org/wiki/Normal_distribution

PDF :

P = integrate pdf(x) from x=0 to 1 = cdf(1)
P = integrate pdf(x) from x=2 to 5 = cdf(5) - cdf(2)
https://www.youtube.com/watch?v=hgtMWR3TFnY

[shannon112]

Central Limit Theorem
https://en.wikipedia.org/wiki/Central_limit_theorem

中央極限定理是機率論中的一組定理。中央極限定理說明，在適當的條件下，大量相互獨立隨機變數的均值經適當標準化後依分布收斂於常態分布。這組定理是數理統計學和誤差分析的理論基礎，指出了大量隨機變數之和近似服從常態分布的條件。
n = sample size
taking several time in sample size to calculate mean/sum/or....
-> stack each time result mean/median/or.... to make a frequency plot
-> which is the sampling distribution of the sample mean/median/or....
-> when n -> very large, we can get a normal distribution
-> its mean/median/or.... close to real, std is smaller when n is larger
https://www.youtube.com/watch?v=JNm3M9cqWyc
https://www.youtube.com/watch?v=FXZ2O1Lv-KE
https://www.youtube.com/watch?v=NYd6wzYkQIM