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Visual Cognition and Modeling Lab

This document summarizes key concepts in probability and statistics. It discusses random variables and outcomes from experiments like flipping coins. It defines probability, random variables, parameters, and distributions like the binomial distribution. It also covers expected values, variance, standard error, sequences of random variables, and concepts like the law of large numbers and sampling distributions.

EducationTechnologySelf Improvement
1 of 42
Chapter 1 Basic Concepts 楊政達
1.1 Random Variables ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Either or 空集合
[object Object]
 
 
聯集 vs 交集
Kolmogorov Axioms of probability
[object Object]
大寫英文字
 
∑ f(x) = 1
 
Matlab code ,[object Object],[object Object],[object Object]
[object Object]
PROBLEM 1.1.1
1.2 Binomial Distribution
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
作業 ,[object Object]
 
[object Object]
y = number of observing successes in N trials
 
Matlab code ,[object Object],[object Object],[object Object]
1.3 Expected Values of Random Variables
Definition 15 (Expected Value) ,[object Object],[object Object]
[object Object],[object Object]
Definition 16 (Variance) ,[object Object],[object Object]
Definition 17 (Standard Error) ,[object Object]
PROBLEM 1.3.1
 
[object Object],[object Object]
1.4 Sequences of Random Variables
Definition 19 (Realization) ,[object Object]
Definition 20 (Relative Frequency Histogram)
 
Law of Large Numbers
 
Definition 21 (Sampling Distribution) ,[object Object]
 

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