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An Illustration of CLT-ECO6416

# An Illustration of CLT-ECO6416 - An Illustration of CLT...

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An Illustration of CLT Sampling Distribution of the Sample Means: Instead of working with individual scores, statisticians often work with means. What happens is that several samples are taken, the mean is computed for each sample, and then the means are used as the data, rather than individual scores being used. The sample is a sampling distribution of the sample means. The central limit theorem explains why many distributions tend to be close to the normal distribution. The key ingredient is that the random variable being observed should be the sum or mean of many independent identically distributed random variables. We can draw the probability distribution of the following random variables: Sampling Distribution of Values (X): Consider the case where a single, fair die is rolled. Here are the values that are possible and their probabilities. X Values 1 2 3 4 5 6 Probability 1/6 1/6 1/6 1/6 1/6 1/6 Here are the mean, and variance of this random variable X: Mean = μ = E[X] = Σ [ x × p(x) ] = 3.5 Variance = σ 2 = E[X 2 ] – μ 2 = Σ [ x 2 × p(x) ] - μ 2 = 2.92 Sampling Distribution of Samples' Mean (Xbar): Consider the case where two fair dice are rolled instead of one. Here are the sums that are possible and their probabilities.

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An Illustration of CLT-ECO6416 - An Illustration of CLT...

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