誉院宾所清怨南鱼王季大門厦黄 Multivariate Probability Distributions Professor Yongmiao Hong Cornell University April 16,2020
Multivariate Probability Distributions Professor Yongmiao Hong Cornell University April 16, 2020
CONTENTS 6.1 Population and Random Sample 6.2 Sampling Distribution of Sample Mean 6.3 Sampling Distribution of Sample Variance 6.4 Student's t-Distribution 6.5 Snedecor's F Distribution 6,6 Sufficient Statistics 6.7 Conclusion Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 2/167
Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 2/167 6.1 Population and Random Sample 6.2 Sampling Distribution of Sample Mean 6.3 Sampling Distribution of Sample Variance 6.4 Student’s t-Distribution 6.5 Snedecor's F Distribution 6.6 Sufficient Statistics 6.7 Conclusion CONTENTS
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Statistical analysis is based on outcomes of a large number of repeated random experiments of same or similar kind. Suppose a random variable Xi denotes the outcome of the i-th experiment.We then obtain a sequence of out- comes,X1,...,Xn,if n experiments are implemented. .This sequence of outcomes then constitutes a so-called random sample from which one can make inference of the underlying probability law which has generated the observed data. Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 3/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 3/167 Population and Random Sample Population and Random Sample
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Definition 1(6.1).[Random Sample] A random sample,denoted as X"=(X1,..,X),is a sequence of n random variables X1,...,Xn. A realization of the random sample X",denoted as x"= (1,,n),is called a data set generated from X"or a sample point of Xr. A random sample Xm can generate many different data sets. The collection of all possible sample points of X"constitutes the sample space of the random sample X". Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 4/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 4/167 Definition 1 (6.1). [Random Sample] Population and Random Sample Population and Random Sample
Introduction to Sampling Theory Population and Random Sample Population and Random Sample Example 1 (6.1).[Throwing n Coins] Let Xi denote the outcome of throwing the i-th coin,with Xi=1 if the head shows up,and Xi=0 if the tail shows up. Then X"=(X1,...,Xn)'constitutes a random sample. If we throw n coins,we will obtain a sequence of real numbers, such as xn=(1,1,0,0,1,0,·,1). This sequence is a data set of size n from the random sample Xn. Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16,2020 5/167
Introduction to Sampling Theory Introduction to Sampling Theory Introduction to Statistics and Econometrics April 16, 2020 5/167 Example 1 (6.1). [Throwing n Coins] Population and Random Sample Population and Random Sample