PS_3_and_Solutions

Since we are taking these samples randomly we do not

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Unformatted text preview: es each of which has observations. Since we are taking these samples randomly, we do not expect these samples 1, … , . to be same, nor do the sample means and sample standard deviations , Therefore, both the sample mean and sample standard deviation are random variables. After collecting samples of size , we have a sample of sample means of size and a sample of sample standard deviations of size as shown in the below figure. You can think that these two samples of size are actually realizations of the population of , population of all possible means of a sample of size drawn from the population of , and the population of , population of all possible standard deviations of a sample of size drawn from the population of . 2 16 March 2011 As we have seen many times, the mean of the sample means is and the standard deviation of the sample means is /√ . Observe that the distribution of each individual from population , is not necessarily same with the distribution of an individual from of , represented by population of . You can see an example of this below. Remember that as the sample size gets larger, the distribution converges to the normal distribution with same parameters according to the Central Limit Theorem (CLT). You will learn about the distribution of each from the population of in the upcoming lectures. The distributions of random variables and are known as sampling distributions. Example: Consider the Question 1 in PS # 2. Observe that we are given all possible outcomes and their correspondi...
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