Semester - III, Model Paper-I


Model Paper - I
Subject: STATISTICS, Paper–III: Statistical Methods
Time: 3 hrs                                                                                                   Max. Marks: 80M
                                                              SECTION - A                                                
Write any Five questions                                                                                         5 X 4 = 20
1. Derive the limits for rank correlation coefficient .
2. Two variables X and Y with 50 pairs of observations found to have mean and standard deviation 10, 3 and 6, 2 respectively and r (x,y) = 0.3. But subsequently it was found that one pair of values X = 10 and Y = 6 were wrong and hence weeded out with remaining 49 pairs of observations, find how much the value of  ‘r' is affected .
3. Define Karl Pearson’s coefficient of contingency .
4. Define consistency. How do you check it for two attributes.
5. Define t-distribution. State its properties.
6. Define sufficiency. State Fisher’s Neyman factorization theorem.
7. Explain the estimation by the method of moments.
8. Explain point and interval estimation.
SECTION - B
Answer all 4 Questions:                                                                                            4 X 15 = 60  
9.  (a). Explain the principle of least squares. Derive the normal equations for fitting of a curve               of the type Y = abx                                                                              (OR)               
     (b). Derive rank correlation coefficient and obtain its limits.
10.(a).Define partial and multiple correlation coefficients. Calculate partial and multiple                        correlation coefficients using the following data.  r12=0.82, r13=0.77, r23=0.80                                                                                            (OR)
     (b). Define Yule’s coefficient of association and colligation. Obtain relationship between                      them.
11.(a).(i).Explain F-distribution with properties and applications.
(ii).Obtain relation between  t and F distributions.                                                                                                    (OR)                                       
     (b).Define unbiasedness. Show that sample variance is not an unbiased estimator of the                      population mean s2.
12.(a).Explain method of maximum likelihood estimation. Obtain M.L.E for the parameter l                of poison distribution.                       (OR)
     (b).Obtain 100(1-a)% confidence interval for m in the normal population, when
 (i). s is known                   (ii). s is unknown
  

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