Lecture3 - Feb 1 st lecture Sampling from the Normal...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Feb 1 st lecture Sampling from the Normal Population * Example : We wish to estimate the distribution of heights of adult US male. It is believed that the height of adult US male follows a normal distribution 2 ( , ) N Def. Simple random sample: A sample in which every subject in the population has the same chance to be selected. X : The Random Variable denote the height of a adult male we will choose randomly from the population So 2 ~ ( , ) X N : the distribution of a randomly selected subject is the population distribution. Theorem 1 Sampling from the normal population Let i.i.d. 2 1 2 , ,..., ~ ( , ) n X X X N , where i.i.d stands for independent and identically distributed 1. 2 ~ ( , ) X N n 2. 2 2 2 1 1 2 2 (X ) ( 1) ~ (Chi Square distribution with ( 1) degrees of freedom), n i i n X n S n =--- =- *Reminder: The Sample variance 2 S is defined as: 2 2 1 (X ) 1 n i i X S n =- =- *Def 1: The Chi-square distribution is a special gamma distribution (*** Please find out...
View Full Document

Page1 / 3

Lecture3 - Feb 1 st lecture Sampling from the Normal...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online