Programming Assignments
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