Total No. of Questions 10] [Total No. of Pages 02
M.Sc. DEGREE EXAMINATION, MAY 2017
First Year
STATISTICS
Design of Experiments
Time 3 Hours Maximum Marks: 70
Answer any Five questions.
All questions carry equal Marks.
Q1) Define:
Rank of a matrix.
ii) Inverse of a matrix.
iii) Idempotent matrix and
iv) Trace of a matrix.
Give examples one each.
State and prove Cauley-Hamilton theorem.
Q2) State Cochran's theorem for quadratic forms. Find the rank of the following
matrix: 3
5 1 3
0 0 2
10 2 4
7
Find the characteristic roots and vectors of A 3
3 −6 6
2 −4 4
1 −2 2
7
Q3) Explain the
Linear model and
ii) Estimable functions.
State and prove Gauss-Markov theorem.
Q4) Explain the
Generalised linear model and
ii) Best linear unbiased estimates.
State and prove Aitken's theorem.
Q5) Explain the analysis of covariance of two-way classification.
Explain the analysis of variance of one-way classification with unequal
number of observations.
Q6) Explain the analysis of covariance of one-way classification.
Explain the analysis of variance of two-way classification with unequal
number of observations.
Q7) Explain the missing plot technique when some observations are missing.
Explain RBD. Obtain the least squares estimates and expectations of
means sums of squares.
Q8) Explain CRD. Obtain the least squares estimates and expectations of means
sums of squares.
Explain
Graeco Latin Square Design and
ii) Mutually orthogonal Latin squares design.
Q9) Explain the analysis of 23 factorial experiment.
Explain the interblock analysis of BIBD.
Q10) Explain the analysis of 32 factorial experiment.
Explain the intrablock analysis of BIBD.