Assignment 1

# Assignment 1 - Stat 5102(Geyer Spring 2010 Homework...

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Stat 5102 (Geyer) Spring 2010 Homework Assignment 1 Due Wednesday, January 27, 2010 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 1-1. For the following data 2.2 0.8 2.0 3.6 3.6 1.8 2.2 1.0 1.2 2.4 1.4 3.2 1.0 1.8 1.6 0.4 0.2 2.0 2.2 2.4 (a) Find the mean of the empirical distribution. (b) Find the variance of the empirical distribution. (c) Find the standard deviation of the empirical distribution. (d) Find the median of the empirical distribution. (e) Find the lower and upper quartiles (the 0.25 and 0.75 quantiles) of the empirical distribution. (f) Plot the empirical distribution function. (g) Find Pr( X < 2 . 5) under the empirical distribution. 1-2. Suppose n is a positive integer, p is a real number such that 0 p 1 and np is an integer. Suppose the data consist of n (1 - p ) zeros and np ones. Show that

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Assignment 1 - Stat 5102(Geyer Spring 2010 Homework...

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