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# prac9stat - QUEEN MARY UNIVERSITY OF LONDON MTH 4106...

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QUEEN MARY, UNIVERSITY OF LONDON MTH 4106 Introduction to Statistics Practical 9 13 March 2012 Today we will draw graphs to show how well the normal distribution approximates the binomial and Poisson distributions, use an example to demonstrate the Law of Large Numbers. You will be asked to include some of these graphs in the Feedback question on the next assignment. 1 (Normal approximation to a symmetric Binomial distribution) If X Bin(9 , 0 . 5) then X has mean 4 . 5, variance 2 . 25 and standard deviation 1 . 5. So it should be well approximated by a normal random variable Y with mean 4 . 5 and standard deviation 1 . 5. We shall plot both of these on the same graph. Use Graph Probability Distribution Plot ... , choose Two Distributions and click OK . Make the first distribution Bin(9 , 0 . 5) and the second distribution N (4 . 5 , 2 . 25), and choose to overlay them on the same graph. You should get a much prettier version of the hand-drawn figure that I showed in lectures.

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