Semester- I, Model Paper -I


Model Paper - I
Subject: STATISTICS
Paper-I:Descriptive Statistics and Probability

Time: 3 hrs                                                                                                            Max. Marks: 80
                                                                 SECTION - A                                             
Write any Five questions:                                                                                         5 X 4 = 20
1. Explain Sheppard corrections for moments.
2. Prove that Karl Pearson’s coefficient of skewness lies between -3 and +3.
3. Give mathematical and axiomatic definitions of probability.
4. State and prove addition theorem of probability for two events.
5. Define distribution function and state its properties.                                  
6. Define one-dimensional random variable. Write the procedure for transformation of
    one-dimensional random variable.
7. State and prove Cauchy Schwartz’s inequality.
8. Define characteristic function and state its properties.
     SECTION - B 
Answer all 4 Questions:                                                                                            4 X 15 = 60

9.  (a).Define primary data. Explain methods of collecting primary data with merits and                       demerits.                                                    ( OR )
     (b).Define central and non-central moments. Establish the relation between moments                         about mean in terms of moments about origin.
10.(a).(i). Define mutually exclusive and exhaustive events. 
           (ii). State and prove addition theorem of probability for ‘n’ events.
                                                                              ( OR )            
     (b).(i). State and prove Boole’s inequality.
            (ii). If P(A˅B) = 5/6, P(A˄B) =  1/3  and  1-P(B) = 1/2, Prove that the events A and B are
               independent.
11.(a).Define random variable. A random variable ‘X’ has the following probability function.
                   X:      0          1          2          3          4          5            6            7
               P(X):     0          k          2k        3k        k         k2         2k2      7k2 +k
            Find (i). Value of  K       
                      (ii). Evaluate P(X  6 , P(X 6) and P(0 X 5)
                      (iii). Distribution function.
                                                                             ( OR )
      (b).Define probability density function. A continuous random variable ‘X’ has the                             following p.d.f           
                                f(x) = A + Bx ; 0  X  1. If its mean is    then
              find  (i). Values of A and B.
                      (ii). Variance of ‘x’.
                      (iii). Distribution function.
12. (a).Define MGF and CGF of a random variable. State and prove their properties.
                                                            (OR)
      (b). (i). State and prove multiplication theorem of expectation.
             (ii). State and prove Chebychev’s  inequality.

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