Utah State University
ECE 6010
Stochastic Processes
Programming Exercise # 1
Due Friday September 9.
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 Matlab function rand generates an independent instance of a stan-
dard Gaussian random variable. That is, randn is a Gaussian random number generator:
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N(0,1). Random column vectors of length nare 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 Matlab.
rand Similarly, the Matlab function rand generates independent uniform U(0,1)random num-
bers. Columnandrowvectorsandmatricesofrandomnumbersaregeneratedusingrand(n,1),
rand(1,n),rand(n,m). For more information type help rand in Matlab.
Histograms The Matlab hist command produces a histogram. This is a representation of the
empirical density function. In ahistogram, a sequence of bins is established. For each value in
a set of data, the number of times that data points fall in a binis counted. In the Matlab hist
command, the histogram is plotted automatically. To see an example of how the histogram
works, type the following in Matlab:
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 x1,x2, . . . , xN, where
each vector is a column vector of length ndrawn independently and identically distributed
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