LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2012

ST 1817 – STATISTICAL COMPUTING – I

 

 

Date : 03-05-2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

1. a) For the following frequency distribution fit a poisson distribution and test the goodness of fit at 5 % level. (12 marks)

 

X	f
0	212
1	128
2	37
3	18
4	3
5	2

 

1. b) The following data gives the frequency of accidents in a city during 100 weeks.

 

No. of accidents	No.of weeks
0	25
1	45
2	19
3	5
4	4
5	2

 

Fit a distribution of the form  P (X = x ) =  for the given data and test goodness of fit at 5 %  level.                                                              (21 marks)

 

 

 

 

 

2. a) Five biased coin were tossed simultaneously 1000 times and at each toss the no. of heads was observed. The following table gives the no.of heads together with its frequency (17 marks)

 

 

X ( no. of heads)	0	1	2	3	4	5
f(x)	38	144	342	287	164	25

 

Fit a binomial distribution to the above data and test whether the fit is good at 5 % level.

 

b)

Travel time Y	9.3	4.8	8.9	6.5	4.2	6.2	7.4	6	7.6	6.1
No.of deliveries	4	3	4	2	2	2	3	4	3	2
Miles travelled	100	50	100	100	50	80	75	65	90	90

 

• Build a multiple linear regression model for the above data.
• Determine                                                                                                  (17 marks)

 

3. a) Find the inverse of the following matrix using partitioning method.

 

 

A =                                                                             (23 marks)

 

1. b) Find the rank of A, where A = (10 marks)

 

 

 

 

4.a)  Determine the characteristic roots and vectors of the matrix

 

(15 marks)

 

1. b) Write the quadratic forms of the matrix

 

 

A =                                                                  (18 marks)

 

5.Compute tolerance and variance inflation factor for each explanatory  variable based on auxiliary regression equation and the  given data .

 

 

 

 

 

 

 

 

 

 

Y
8	5.2	5.1	2.3
9	5.6	5.2	1.2
7	4.8	4.7	1.5
5	4	3.2	1.6
6	6	3.2	1.4
4	5	5.4	1.8
5	4.5	3.9	1.9
2	2.3	2.6	1.8
1	1.5	1.8	1.5
3	2.6	2.1	1.6

 

(33 marks)

 

 

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