Probability and Statistics Course | Khan Academy about awesome-ros-mobile-robot HOT 3 OPEN

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

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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

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

**極限定理是機率論中的一組定理。**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

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