Unit wise important questions

B.Sc (M.S.Cs)-III Year                                        Subject: Statistics, Paper: III

UNIT-I

1. Explain the principal steps involved in a sample survey.

2. (i).  Distinguish between SRSWOR and SRSWR with examples.

(ii). In SRSWOR, show that the Probability of selecting a specified unit  at   any given draw is equal to the probability of  selecting it at the first draw.

3. In SRSWOR, show that

       (i). Sample mean square is an unbiased estimator of population mean square.

       (ii). V(_n)= {(N-n)/Nn} S²

    

4. Explain the purpose of stratification in sample survey.

        Show that V(_n)_R  V(_st)_prop in usual notations.

     

 5. In usual notations, prove that the systematic sample mean is more efficient
    than the mean of a simple random sample taken without replacement

     if   S²_wsy  S².

 6. With the usual notations, Prove that  V(_st)_opt  V(_st)_prop  V(_n)_wor

 7. In Neyman allocation of stratified random sampling prove that V(_st) is        minimum for fixed total sample size n if n_i  N_i S_i .

8. In stratified random sampling , optimum allocation. Prove that, V(_st) is             minimum if  n_i  N_i S_i / _i

   

 9. If a population consists of a linear trend , then  prove that  

    V(Y_st) < V(Y_sys) <V(Y_n)_R      

     

10. Explain sampling and non-sampling errors.

UNIT-II

1. Explain the statistical analysis of one way classification.

2. Describe the technique of the analysis of variance. Explain ANOVA two way classification.

3. Explain the principles of experimental design.

4. Explain the missing plot technique in RBD.

 5. Explain M*M Latin square design.

 6. Explain efficiency of RBD over CRD.

7. Explain efficiency of LSD over RBD.

 8. Explain the missing plot technique in LSD.

 9. Derive expectation of various sum of squares one way classification.

 10. Explain statistical analysis of CRD with merits and demerits.

UNIT-III

1. What are the components of time series mention its uses.

2. Explain secular trend in time series and give the methods of semi-average and moving averages for measuring trend.

3. What are seasonal variations?.Explain ratio to trend method for measuring seasonal variations.

4. Explain link relative and ratio to moving averages methods for measuring seasonal variations.

5. How do you fit a modified exponential curve and Gompertz curve to a time   series data.

6. What is logistic curve? Explain various methods of fitting logistic curve.

7. What are the economic barometers? Discuss their advantages as well as the limitations.

8. Define Index numbers. Describe steps in construction of index numbers.

9. What is cost of living index number? Explain the steps in the construction of cost of living index number. Mention the uses.

10. Explain consistency tests for index numbers. Prove that fisher index number is an ideal index number.

11. Explain the concepts of base shifting, splicing, and deflation of index numbers.

12. Define national income. Explain the difficulties in estimation of national income.

13. What are the functions of CSO and NSSO.

UNIT-IV

1. Explain various rates of measuring mortality. Discuss its merits and demerits.

2. Explain the difference between crude death rate and standardizing death rate. Give briefly the direct and indirect method of finding standardizing death rates.

3. Define life table. Explain in detail the construction and uses of life tables.

4. Explain various measures of fertility. Discuss merits and demerits of these measures.

5. Explain GRR and NRR for measuring population growth.

6.Define demand, supply, equilibrium price. Describe demand and supply curves.

7. Describe Leontief’s method of estimating price elasticity of demand for time series data and give its assumptions and limitations.

8. Describe Pigou’s method of estimating price elasticity of demand for time series data and give its limitations.

9. Define demand function. Explain constant price elasticity of demand.

10. Describe Pareto’s law of income distribution. Give two few situations where Pareto’s law holds good.

Unit wise important questions

B.Sc (M.S.Cs)-III Year                              Subject: Statistics, Paper: IV

UNIT-I

1. What is meant by statistical quality control? Discuss briefly its need and utility in industry.

2. Give the statistical basis for Schewartz control charts. Explain the construction of control chart for Mean and Range.

3. Distinguish between defect and defective. Explain the statistical basis and construction of ‘p’ and ‘np’ charts.

4. What do you understand by control charts for variables? Give the construction of mean and S.D chart.

5. Explain the construction of control chart for number of defects and give applications of ‘C’ chart.

6. Explain the construction of p chart for fixed and varying sample sizes.

7. Explain the construction of np chart for fixed and varying sample sizes.

8. Explain the concepts of process capability index and six-sigma.

9. Distinguish between control limits, specification limits and tolerance limits.

UNIT-II

1. Define the terms AQL, LTPD, consumer’s risk and producer’s risk.

2. Distinguish between process control and product control. State the different types of acceptance sampling plans explaining their merits and demerits.

3. Explain single sampling plan procedure for attributes and obtain its OC and ASN functions.

4. Explain double sampling plan procedure for attributes with OC and ASN curves.

5. Define   i).Reliability   ii).Hazard rate  iii).Failure density  iv).Series and parallel configurations.

6. Explain exponential distribution as life model and its lack of memory property in view of reliability.

7. Explain the method to compute the reliability of a system having series configuration and parallel configuration.

8.Explain series system, parallel system, and k out of n system with examples.

Note: Problems on Reliability are also important.

UNIT-III

1. Explain the scope of operations research.

2. Define the following terms   a) basic solution   b) basic feasible solution 

    c) degenerate solution   d) optimum solution

3. Define convex set and state their properties. State and prove fundamental theorem of LPP.

4. (i). Explain the procedure of graphical method for solving a LPP.

    (ii). Define OR. Explain canonical and standard forms of LPP.

5. When are artificial variables used? Explain two-phase simplex method of solving a LPP.

6. Give the simplex algorithm to solve a LPP.

7. Explain the concept of duality and dual-primal relationship with an example.

8. Explain dual of a symmetric LPP. Show that dual of a dual is a primal with an example.

9. What is degeneracy in LPP? When does it occur? How is it resolved?

10. What are surplus and artificial variables? Explain Big-M method to solve a LPP.

UNIT-IV

1. Stating important assumption define Transportation problem. Explain VAM for obtaining initial basic feasible solution of a transportation problem.

2. Define balanced and unbalanced transportation problem. Explain NWCR and MMM for obtaining initial basic feasible solution of a TP.

3. Explain MODI method of solving TP for optimum solution.

4. Explain transportation problem and show that it is a special case of LPP.

5. What is degeneracy in transportation problem? How is it resolved?.

6. Define assignment problem as a special case of LPP and TP. Explain Hungarian method to solve an assignment problem.

7. (i). How an unbalanced Assignment and Transportation problems are  balanced? Explain with examples.

    (ii). How an assignment problem for maximization is solved? Explain.

8. Explain stepping stone method to obtain an optimum solution for a balanced transportation problem.

9. What is sequencing problem? Give Johnson’s algorithm to solve two machine ‘n’ jobs sequencing problem.

10. Explain the job sequencing algorithm for n jobs on three machines.

11. Explain the procedure of travelling salesman problem and transshipment problem.

Note: Unit III and IV  Problems are also important.