Total No. of Questions 10] [Total No. of Pages 01
M.Sc. DEGREE EXAMINATION, MAY 2018
First Year
STATISTICS
Design of Experiments
Time 3 Hours Maximum Marks :70
Answer any five questions.
All questions carry equal marks.
Q1) Explain the characteristic roots and vectors of a matrix.
State and prove Cauley Hamilton theorem.
Q2) Derive the inverse of the matrix
2 1 4
4 0 2
3 2 7
A
−

−
Explain Coehran's theorem for quadratic forms.
Q3) Explain linear models with examples.
State and prove Gauss Markov theorem.
Q4) State and prove Atken's theorem.
What is best linear unbiased estimate? Explain in brief.
Q5) Explain two-way ANOVA with an example.
What are random effect models? Explain analysis of variance of three way
classification.
Q6) What is meant by two-way, three-way classification? Explain analysis of covariance
of two-way classification.
What are the objectives of ANOVA? Explain its practical applications.
Q7) What is an experiment? Explain the formulation of hypothesis in
experiments.
Explain the principles of randomized block design.
Q8) What is meant by mutually orthogonal Latin Squares? Explain its procedure.
Describe missing plot technique? Explain its applications.
Q9) What is the importance of factorial experiments? Explain.
Explain the analysis of 32 factorial experiment.
Q10)a) Discuss is brief about intra block analysis of BIBD.
Explain the analysis of 23 factorial experiment.