PS_3_and_Solutions

You will rememberthatwehavecalculatedthesevaluesas

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Unformatted text preview: ng probabilities are given to us. This means we can calculate the population mean and standard deviation. You will remember that we have calculated these values as 5,3 and 0,81. 3 5,3; Then we can say that x P(X = x) 16 March 2011 0,81 is the following discrete distribution: 4 0,2 5 0,4 6 0,3 7 0,1 The parameters of the sampling distribution of mean were calculated as follows: 0,81 36 5,3 and 0,0225. Then we can say that 5,3; 0,0225 . Moreover, we can say that is not a discrete probability distribution since mean of a sample that consists of discrete values can take continuous values. Moreover, according to the CLT, as the size of the samples gets larger, we should see that 5,3; 0,0225 ~ 5,3; 0,0225 . As a result, we can conclude that for this example . This shows that sampling distribution and the population distribution are not necessarily the same. Using the probability distribution for the population of given in this example, we can make simulation in a statistical package called R. In the simulation, we want to see what is happening with the sampling distribution, as the sample size gets larger. For this purpose, we take 10000 different samples from the population of and calculate their means. Hence we will have a sample of size 10000 that is drawn from the population of . Since we have large sample of , we can have quite good insight about the distribution of the population of when we plot a histogram of this sample. According to the theoretical discussion above, if we increase the sample size , we expect to see that this distribution tends to be Normal. Therefore, in order to see whether the histogram of the sample...
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