Total No. of Questions 10] [Total No. of Pages 02
M.Sc. DEGREE EXAMINATION, MAY 2018
Second Year
STATISTICS
Multivariate Analysis
Time 3 Hours Maximum Marks :70
Answer any five questions.
All questions carry equal marks.
Q1) What is multivariate normal Distribution? Explain its properties.
Obtain maximum likelihood estimators of mean vector in a P-variate normal.
Q2) State and prove a necessary and sufficient conditions for one set of random
variables and subset consisting of the remaining variables in a P-variate
normal to be independent.
Obtain the distributions of sample mean and sample covariance matrix in a Pvariate
model.
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 the procedure of MANOVA for one-way classification.
Evaluate T2, for testing H0 using the data
12 8 6 8
12 9 9 10
X



.
Q5) Explain oblique rotation and orthogonal rotation of factors.
What is factor analysis? Explain the procedure of factor analysis.
Q6) State and prove the properties of principle components.
What is the purpose of factor rotation? Explain orthogonal factor rotation and
oblique factor rotation.
Q7) What is discriminant analysis? Explain how it is different from factor
analysis.
Discuss the Fisher's method for classification into one of several problems.
Q8) Discuss the problem of classification with several multivariate normal
populations.
If B is defined as −μ2 −μ2 for some constant verify that
1
1 2 e cΣ− is infact an Eigen vector of 1 Σ− where Σ is an covariance
matrix.
Q9) What is cluster analysis? Explain its procedure.
Explain single Linkage, complete Linkage and average Linkage methods.
Q10)a) Explain the difference between hierarchical and non-hierarchical methods of
clustering. Explain K-means method.
Discuss the similarity measures.