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# Programming Assignments

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Introduction   ::   Exercises

## Introduction

This exercise will provide an opportunity to do some calculations and plots with actual data. The intent is to make some of the abstract concepts a little more concrete. This exercise is to be done using MATLAB.

## Background

randn

Every call to the M ATLAB function rand generates an independent instance of a standard Gaussian random variable. That is, randn is a Gaussian random number generator: . Random column vectors of length n are generated by randn(n,1) . Row vectors are generated with randn(1,n) . A matrix of random numbers is generated with randn(n,m) . For more information, type help randn in M ATLAB .

rand
Similarly, the M ATLAB function rand generates independent uniform random numbers. Column and row vectors and matrices of random numbers are generated using rand(n,1) , rand(1,n) , rand(n,m) . For more information type help rand in M ATLAB .

Histograms
The M ATLAB hist command produces a histogram. This is a representation of the empirical density function. In a histogram, a sequence of bins is established. For each value in a set of data, the number of times that data points fall in a bin is counted. In the M ATLAB hist command, the histogram is plotted automatically. To see an example of how the histogram works, type the following in M ATLAB :
              x = randn(1,1000);   % create a vector of 1000 Gaussian random numbers
hist(x,20);  % plot the histogram with 20 bins
hist(x,100); % plot the histogram with 100 bins


Estimating mean and covariance
Given a sequence of vector observations , where each vector is a column vector of length drawn independently and identically distributed according to some distribution, the sample mean of the distribution is

The sample covariance is