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Subject: STATISTICS, Paper-IV: Inference Time: 3 hrs                                                                                                          Max. Marks: 80                                                                  SECTION- A         I. Answer any Five questions:                                                                                     5*4=20M 1.     Define types of errors. 2.     Write a short note on randomized and non randomized test functions. 3.     Define level of significance, power of the test. 4.     Explain clearly the procedure generally followed in testing of a hypothesis. 5.     Explain test for randomness. 6.     Explain large sample test procedure for single proportion. 7.     Define interval and ratio scale. 8.     What is meant by non parametric methods. SECTION –B   II. Answer all questions:                                                                                              4*15=60M 9(a )

SECTION - A I. Answer any Five questions :                                                                  5 X 3=15M 1. Define OR & Explain its scope of OR. 2. Explain the procedure of VAM method. 3. Explain the procedure of Big M-Method. 4. Solve the following LPP graphically Min z= -6X 1 -4X 2    subject to the constraints 2X 1 +3X 2  >=   30 ,   3X 1 +2X 2 <= 24   ,   X 1 +X 2  >=3  and   X 1 , X 2 0 . 5. State and prove fundamental theorem of LPP. 6. Explain the concept of Travelling salesman problem. 7. Concept of Transhipment problem. 8. Explain sequencing problem. SECTION – B Answer all Three Questions:                                                                    3 X 15 = 45    9.(a). I. When artificial variables are used. Explain Two Phase method of solving LPP.           II. Explain the procedure of Graphical method.                                                             (OR)   (b). Solve the following LP

SECTION - A Answer any Five questions :                                                                   (5*4=20M)        1. Define Binomial distribution. Obtain mean and variance. 2. Derive mode of Poisson distribution. 3. Derive m.g.f of Poisson distribution. Hence find mean and variance. 4. Define Exponential distribution. Obtain mean and variance. 5. Obtain median of the Normal Distribution. 6. State Central limit theorem 7. Define Beta Distribution of 1 st and 2 nd kind. 8. State and prove Additive property of Geometric distribution. SECTION - B Answer all four questions :                                                                     (4*15=60M) 9.(a).Define Poisson distribution. Derive Recurrence relation for moments of Poisson             distribution.                                                                     (OR)    (b). Prove that Poisson distribution is the limiting of Binomial distribution by             stating the condit