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Posted Date: 28 Apr 2008 Posted By:: sac Member Level: Gold Points: 5 (Rs. 1)
2007 Alagappa University M.Sc Computer Science Mathematics Question paper
M.Sc. DEGREE EXAMINATION, DECEMBER 2007.
Time : Three hours Maximum : 100 marks
Answer any FIVE questions.
All questions 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 given X = x
(b) The joint p.d.f of two variables X and Y is given by .
Find the marginal distributions of and Y.
2. (a) State and prove weak law of large numbers.
(b) State and prove Bernovlli's law of large numbers.
3. (a) If and are two 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 two types of errors.
(b) State and prove Neyman Pearson lemma.
6. Explain the test for the equality of means of two normal populations.
7. A variable trial was conducted on wheat with 4 varieties in a Latin squar design. The plan of the experiment and the per plot yield are given below :
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 result.
8. (a) Explain and p charts.
(b) Given below are the values of sample mean and sample range R for 10 samples, each of size 5. Draw the appropriate 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
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