Page 66 - Introduction to Statistical Pattern Recognition
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48 Introduction to Statistical Pattern Recognition
n A
3. Compute the sample mean, M, and sample covariance matrix,,C
,.
4. Repeat 1 and 3, 10 times. Compute the sample mean and sample variance
A
for each component of M and C over 10 trials.
5. Repeat 4 for N =lo, 20, and 40, and examine the effect of the sample size.
6. Simultaneously diagonalize X and and form a vector V = [XI &I7
Compute the sample mean and sample covariance of V over IO trials.
Problems
1. Compute and plot q I (x) and q2(x) forp I (x) =N,,(O, 1) andp2(x) =A',( 1,2).
2. Let p (X) be Nx(M, C) with
Show that
p (x I ) = N.,, (m 1, 0:) (a marginal density) ,
3. For the distribution of Problem 2, plot the contour lines for
d2(X) = 1, 4, and 9 ,
where the parameters are selected as
p=-l, -0.5,0,0.5, 1.
