M.Sc. (Statistics) (Semester III) (CBCS) Examination, 2017
Multivariate Analysis (Paper XII)
Day Date: Thursday, 20-04-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
N.B. Q.1 and Q.2 are compulsory.
Attempt any three questions from Q. 3 to Q.7.
Figures to the right indicate full marks.
Q.1 Choose the correct alternative: 05
simple correlations between the variables and
factors.
Factor scores Factor loadings
Correlation loadings both a and b are correct
Suppose X is a p dimensional random vector with variance
covariance . If e1, e2,…..,ep represent p orthogonal eigen
vectors of corresponding to eigen values
respectively then which of the following
is not true?
First principle component is e1X1 Var (e1X1)
e1X1 and e2X2 are correlated
Let X1, X2,…, Xn be a random sample of size n from p-variate
normal distribution with mean vector and covariance matrix
. Then √ is approximately distributed as





Let p dimensional vector X has distribution. Let us
partition in q and p-q component sub vectors.
Then conditional covariance of given is




Let X be a random vector with covariance matrix . Decrease
in variances of p variables in X will lead to
Increase trace decrease trace
does not affect trace nothing can said
Fill in the blank: 05
Matrix of regression coefficient of on is
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Generalized variance is covariance matrix.
Mahalanobis squared distance between two normal
populations and is
Hotelling's is nonsingular transformation.
Sample covariance matrix S is ____estimator of .
State true or false: 04
In oblique rotation the rotated factors will be correlated.
Cluster analysis reduces the number of variables.
The diagonal sub matrices of Wishart matrix have a normal
distribution.
Marginal normality always implies multivariable normality.
Q.2 Answer the following:
Define Hotelling's stastistic and Wishart matrix.
Let vector X be distributed according to then show
that is distributed as
06
Write short notes on the following:
Additive property of Wishart matrices
Partial correlations
08
Q.3 Let Obtain characteristics function of X. 07
Based on random sample of size n from distribution,
obtain a LRT for testing against
07
Q.4 Obtain the distribution of Wishart matrix in canonical case. 07
Let In usual notations show that random
vectors and are independent if and only if
07
Q.5 Describe the problem of classification. Derive Fisher's best linear
discriminant function.
07
Discuss orthogonal factor model with m common factors. 07
Q.6 Define principal components. State and prove its properties. 07
Obtain all principal components if
Also obtain the
percentage of variation explained by these components.
07
Q.7 Define pair of canonical variables and canonical correlations.
Establish the relationship of canonical correlation with multiple
correlations.
07
Discuss with illustration the single linkage clustering method. 07