Answered: Use R to illustrate the WLLN (weak law…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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Use R to illustrate the WLLN (weak law of large numbers): draw a random sample from the exponential, normal, Poisson, and uniform distributions—each with mean ? = 5 (note that this would leave you some leeway in the normal and uniform cases—set the parameters for these distributions so the standard deviation is also 5.) Be careful with the exponential, since it is specified by rate, so you’ll make a call to R of: rexp(n,rate=1/5) to specify a mean of 5. Let the sample size for each grow sufficiently large to show the WLLN: that the sample mean approaches the true (theoretic) mean.

Expert Solution

Step 1

WLLN: WLLN says that as we increased the sample size of the sample collected from specified distribution, sample mean reaches to true population mean of the distribution.

Here we will select sample of sizes 5, 10, 20, 50, 100, 500, 1000, 5000, 10000, 100000 record the sample mean every time and will se that in each case exponential, normal, Poisson, and uniform distributions the sample mean approaches to population mean.

Note: we will select distribution such that all having population mean = 5.