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Unformatted text preview: Statistics 113 Lab 2: Central limit theorem Nigel Chou Lab Section 02D ________________________ Problem 1: Commented code included at end of assignment. Discussion of part 1: For the Binomial distribution (drawb), holding n constant, when p is close to 0 and 1, the histogram does not approximate the normal distribution by CLT very well. The approximation gets better as p gets closer to 0.5, as can be seen in Figure 1. Also, as p approaches 0.5 from 0 and 1, the variance increases while the peak values of both the histogram and the normal distribution become smaller. At the same time, the spread of the histogram and the normal distribution relative to the range of x (which for these plots is 20 times the variance of x_bar) decreases and the distribution becomes more concentrated at the mean (which is always given by np). As n increases with p held constant, the histogram approximates the normal distribution by CLT...
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 Fall '08
 MUKHERJEE
 Statistics, Binomial, Central Limit Theorem, Normal Distribution, Probability theory, Binomial distribution, Cauchy distribution

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