Lecture7_412 - AMS412 Professor Wei Zhu Sampling from the...

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1 AMS412 Professor Wei Zhu 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 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 : the distribution of a randomly selected subject is the population distribution. Theorem 1 Sampling from the normal population Let , where i.i.d stands for independent and identically distributed 1. 2. A function of the sample variance as shown below follows the Chi square distribution with (n-1) degrees of freedom: *Reminder: The Sample variance is defined as: *Def 1: The Chi-square distribution is a special gamma distribution (*** Please find out which one it is.) *Def 2: Let , then 3. are independent .
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