Total No. of Questions 10] [Total No. of Pages 02
M.Sc. DEGREE EXAMINATION, MAY 2017
Second Year
STATISTICS
Multivariate Analysis
Time 3 Hours Maximum Marks: 70
Answer any FIVE questions
All questions carry equal marks
Q1) Define a p-variate normal distribution. Obtain its marginal and conditional
distributions.
Obtain the distributions of sample mean and sample covariance matrix in a
p-variate normal.
Q2) Obtain the m.l estimators of the mean vector and the covariance matrix in a
p-variate normal.
State and prove a necessary and sufficient condition for one set of the
random variables and the subset consisting of the remaining variables in a pvariate
normal to be independent.
Q3) Derive the null distribution of T2.
Develop a test statistic for testing the hypothesis that the mean vector is a
given vector. Obtain the confidence region for the mean vector.
Q4) Explain MANOVA for one-way classification.
Explain likelihood ratio test for testing the hypothesis that the mean vectors
and covariance matrices are the same.
Q5) Define principal components. Derive the expressions for the first and second
principal components.
Explain principal factor method of estimation for estimating factor loadings.
Q6) State and prove the properties of principal components.
Explain oblique rotation and orthogonal rotation of factors.
Q7) Detail tests associated with discriminant functions.
Explain the problem of classification with several multivariate populations.
Q8) Discuss the problem of classification of observations.
Explain the problem of classification into one of the two known multivariate
normal populations.
Q9) Explain the concept of cluster analysis and its uses.
Explain
K-means method and
ii) average linkage method
Q10) Discuss the similarity measures.
Explain any two linkage methods.