Let ,
and
be partitioned as
,
and
. Then derive the conditional distribution of
.
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Let ,
and
be partitioned as
,
and
. Then derive the conditional distribution of
.
Let two independent samples of size and
from trivariate normal populations have following mean vectors and variance-covariance matrices:
and
and
, respectively.
---$
$
samples are significantly different from each other at 5% level of significance or not.$
Define clustering. Differentiate between single linkage and complete linkage method of clustering.
(b) Consider the following partitioned sample variance-covariance matrix S, obtained from a sample of size 10.$
If , then test for the independence of the sub-vectors
and
.
(Use
)
---
Let , where
and
.
Then find and
.
If with
and
. Then find the joint distribution
of X1 + 2X2, 2X1 - X2 and X3.
Obtain the square root matrix corresponding to a matrix . Also
verify that .
Let , where
and
. Check the independence
of (i) X2 and X1 (ii) (X2, X4) and (X1, X3) (iii) (X1, X2) and (X3, X4).