Loyola College M.Sc. Statistics April 2011 Statistical Computing I Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034      LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034    M.Sc. DEGREE EXAMINATION – STATISTICSFIRST SEMESTER – APRIL 2011ST 18167 – STATISTICAL COMPUTING  I
Date : 20-04-2011 Dept. No.   Max. : 100 Marks    Time :                                              Answer all the questions              (4 x 25 =100 Marks)
1 a)  The following frequency distribution gives the number of albino children in families of five children          having at least 1 albino child:No. of Albinos (x) No. of Families (f)1 222 263 94 25 1
Fit a truncated binomial distribution for the above frequency distribution and test the goodness of          fit  at 5% level.
b)  Fit a normal distribution to the following data by area method   and   test   the goodness   of  fit               at 5%  level of significance:x f40 – 60 860 – 80 1280 – 100 20100 – 120 25120 – 140 45140 – 160 22160 – 180 16180 – 200 16200 – 220 4
( 15 +10)    (OR)
c) The table below gives the frequency distribution of the number  of dust nuclei in a small volume         of air that fell on to a stage in a chamber containing moister and filtered air: No.  of dust nuclei (x) 1 2 3 4 5 6 7 8f 60 84 98 70 37 20 5 3
It is suspected that a number of zero counts were wrongly rejected on the ground that the apparatus   was not working and hence not recorded.  Fit a truncated Poisson distribution to the above frequency distribution and test the goodness of fit.
d)   For the following frequency distribution, fit a negative binomial distribution and test the            goodness    of fit  at 5% level: x 0 1 2 3 4 5f 212 128 40 15 3 2

2  a)  Generate a sample of size 5 from the  Bivariate  normal distribution given below:     (OR)       b) Given the three selected points U1,    U2 and    U3 corresponding to t1 = 2 , t2 = 30 and                         t3 = 58 as follows:           t1 = 2,                U1 = 55.8               t2 = 30,             U2 = 138.6                t3 = 58,             U3 = 251.8
Fit a logistic curve by the method of selected points. Also obtain the trend values         for t = 5, 18, 25, 35, 46, 50, 54, 60, 66, 70.
3. a)Find the inverse of the following matrix A using partitioning method:                     A =      (Or)         b) (i)  Obtain the Rank, Index and Signature of the following matrix A:                          A  =
(ii) Verify whether or not the following matrix is negative definite:
B  =                                                                                     (15 + 10)
4)     a) Determine Tolerance and Variance Inflation Factor(VIF) for each explanatory variable based               on the data and fitted auxiliary regression equations given below:Y 8 9 7 5 6 4 5 2 1 3X1 5.2 5.6 4.8 4 6 5 4.5 2.3 1.5 2.6X2 5.1 5.2 4.7 3.2 3.2 5.4 3.9 2.6 1.8 2.1X3 2.3 1.2 1.5 1.6 1.4 1.8 1.9 1.8 1.5 1.6

Fitted Auxiliary regression equations areX1 = 2.211 + 0.95X2 -0.961X3X2 = -0.805 + 0.704X1 + 0.966X3X3 = 1.568 – 0.102 X1 + 0.139X2
(OR)
Y 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1X1 2.45 1.2 2.5 2.14 1.6 2.19 2.1 2.8 1.5 2.8 2.18 1.1 2.22 2.23 1.5 2.11 2 1.9 1.4 2.7X2 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1X3 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0b) Consider the following data and the fitted Logistic regression model  Determine the following:(i) Optimal Cut point based on Gains table                                                        (ii)     Classification table based on the optimal cut point , Sensitivity and Specificity.(18+7)

 

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