LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

BA 26

M.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – November 2008

    ST 3810 – STATISTICAL COMPUTING – II

 

 

 

Date : 07-11-08                 Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

Answer ALL the questions:                                                                         ( 5 x 20 = 100 )

 

1).(a) Let X ~ N₄    , compute

b). Two independent samples observation are drawn from a bivariate normal distribution with common population variance matrix. Test whether the two groups have the same population mean vector.

 

Group A

Age	55	58	59	60	62	65	68
Bp	120	125	130	100	105	120	116
Glucose	140	145	155	158	162	170	180

 

Group B

Age	59	62	58	57	56	69	65	62
Bp	100	126	95	100	105	110	115	120
Glucose	145	155	148	142	143	160	159	156

 

2). (a) Let X be normally distributed according as  N₃ ( ,

with .

Find conditional distribution (X₁ | X₂   = 8, X₃ = 5).

b). Find the maximum likelihood estimator of the 2 x  1   mean vector   and  2 x 2 covariance matrix  based on the random sample  from the bivariate normal population.

c). Income in excess of Rs. 2000 of people in a city is distributed as exponential  20 people were selected and their incomes are shown below

2200	3250	8000	8500	9500
2500	4500	6200	6000	8100
3000	7500	2100	7200	3700
2750	10000	9000	8600	97500

 

Obtain the point estimate of the expected income of a person in this city by maximum likelihood method. Obtain the estimate of its variance.

 

3) (a)  The biologist who studies the spiders was interested in comparing the lengths of female and male green, lynx spiders. Assume that the length X of the female spider is approximately distributed as       and the length Y of the male spider is approximately distributed as . Find an approximately 95 % confidence interval for () using 30 observation of X.

 

 

5.2	4.7	5.75	7.5	6.45	6.55	4.7	4.8	5.95	5.2
6.35	6.95	5.7	6.2	5.4	6.2	5.85	6.8	5.65	5.5
5.65	5.85	5.75	6.35	5.75	5.95	5.9	7	6.1	5.8

 

and the 30 observation of Y ,

 

8.25	9.95	5.9	6.55	8.45	7.55	9.8	10.9	6.6	7.55
8.1	9.1	6.1	9.3	8.75	7	7.8	8	9	6.3
8.35	8.7	8	7.5	9.5	8.3	7.05	8.3	7.95	9.6

Where measures are  in millimeters.

 

(b) .Given below are the qualities of 10 items ( in proper units) produced by two processors A and B.Test whether the variability of the quantity may be taken to be the same for the two processors

Processor A	33	37	35	36	35	34	34	35	33	33
Processor B	38	35	37	38	33	32	37	36	35	37

 

4). (a). For a 3 state Markov Chain with state {0, 1, 2,} and TPM

find the mean recurrence times.

 

• From the following population of 10 clusters compare the following sampling designs for the estimation of the population total

(i)  Select 5 clusters by SRSWTR method

(ii) Draw an SRSWTR of 8 clusters and select a SRSWTR of size 2 from each

cluster and comment upon your results

 

C luster No.		Values    of the	variates
1	345	123	345	456
2	256	345	367	345
3	321	145	456	256
4	267	235	387	478
5	378	378	367	245
6	409	254	390	346
7	236	378	342	234
8	265	456	234	290
9	234	321	345	456
10	267	149	456	345

 

 

5) A sample survey was conducted with the aim of estimating the total yield of paddy. The area is divided into three strata and from each stratum, 4 plots are selected using SRSWTR. From the data given below,  calculate an estimate of the total yield along with an estimate of its variance.

 

Stratum No.	Total No. of Plots	Yield of Paddy for 4 Plots in the sample ( Kgs )
I	200	120	140	160	50
II	105	140	80	200	140
III	88	110	300	80	130

 

 

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