a) Properties of random variables can be explored empirically using Monte Carlo

Question

a) Properties of random variables can be explored empirically using Monte Carlo simulation. Create a dataset with 1,000 rows and 9 columns of exponential random numbers with ? = 1. Compute the minimum of each row in the 10th column. Determine the distribution of the minimum of 9 exponential random variables. Show a screen shot with 4 panels: the data window and 3 plots that justify your choice of distribution: a probability plot, a histogram with your selected distribution superimposed, and an empirical cumulative distribution plot with your selected distribution superimposed. b) Now repeat part (a) for the sum of 9 unit exponentials. Use the same data; just change C10. c) Much statistical theory assumes that data have a normal distribution. Exponential variables can be transformed so that they look much more normal. Consider the family of "power transformations" Y = X1/p, where p > 0. When X has an exponential distribution, find a value of p that transforms the distribution as close to normal as you can make it. Report your choice of p. Then show your results graphically in two ways. First, show a graphics window with two normal probability plots, one showing the original exponential data, the other showing the transformed data. Second, do the same thing with histograms that have normal distributions superimposed.

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This might help you http://vfu.bg/en/e-Learning/Math--Soong_Fundamentals_of_probability_and_statistics_for_engineers.pdf

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