Alagappa University 2007 M.Sc Computer Science Mathematics - Question Paper

DISTANCE EDUCATION
M.Sc. DEGREE EXAMINATION, DECEMBER 2007.
Mathematics
MATHEMATICAL STATISTICS
Time : 3 hours Maximum : 100 marks
ans any 5 ques..
All ques. carry equal marks.
1. (a) Two discrete random variables X and Y have the joint p.d.f where and p are constants with .
(i) Find the marginal p.d.f. of X and Y
(ii) The conditional p.d.f of Y provided X = x
(b) The joint p.d.f of 2 variables X and Y is provided by .
Find the marginal distributions of and Y.
2. (a) State and prove weak legal regulations of large numbers.
(b) State and prove Bernovlli's legal regulations of large numbers.
3. (a) If and are 2 independent –variates with and d.f. respectively then show that is a variate.
(b) State and prove central limit theorem.
4. (a) Derive student's t-distribution.
(b) Obtain the M.L.Es for and for the rectangular population
5. (a) Explain the 2 kinds of errors.
(b) State and prove Neyman Pearson lemma.
6. Explain the test for the equality of means of 2 normal populations.
7. A variable trial was conducted on wheat with four varieties in a Latin squar design. The plan of the experiment and the per plot yield are provided beneath :
C 25 B 23 A 20 D 20
A 19 D 19 C 21 B 18
B 19 A 14 D 17 C 20
D 17 C 20 B 21 A 15
Analyze data and interpret the outcome.
8. (a) Explain and p charts.
(b) Given beneath are the values of sample mean and sample range R for 10 samples, every of size 5. Draw the improper mean and Range charts and comment on the state of control of the process :
Sample No. : 1 2 3 4 5 6 7 8 9 10
Mean : 43 49 37 44 45 37 51 46 43 47
Range : 5 6 5 7 7 4 8 6 4 6

Earning:   Approval pending.