Academic year:

## Units and Topics

# | Unit/Topic | Marks |
---|---|---|

100 | Vital Statistics | - |

200 | Index Numbers | - |

300 | Time Series Analysis | - |

400 | Interpolation and Extrapolation | - |

500 | Theoretical Distributions | - |

600 | Statistical Inference | - |

700 | Statistical Quality Control | - |

800 | Operations Research | - |

Total | - |

## Syllabus

100 Vital Statistics

- Meaning of demography and Vital statistics. Methods of collection of Vital Statistics and uses. Fertility, growth and mortality rates. Life table. Definition of fertiliy and fecundity. Fertility rates- CBR, ASFR, GFR and TFR - definition, merits and demerits, computation. Growth rate- Gross reproduction rate and Net reproduction rate – definition, merits and demerits, computation. Mortality rates- CDR, ASDR, S.T.D.R., IMR, NMR and MMR – definition, merits and demerits, computation. Life table- Meaning and uses. Components of a life table- Explanation of the columns of a life table and simple problems on survival ratio, mortality ratio, average number of survivals and life expectancy.

200 Index Numbers

- Meaning of an index number, characteristics, uses and limitations, brief description of the steps in the construction of a price index number, classification of index numbers as simple and weighted (AM, GM and Aggrigative) index numbers. Price, Quantity and Value index numbers. Construction of unweighted and weighted price index numbers. Construction of Laspeyre’s, Paasche’s, MarshallEdgeworth’s, Dorbish-Bowley’s and Fisher’s Price and quantity index numbers. Construction of Kelly’s price index number. Bias in an index number.
- Testing the appropriateness of an index number - Time reversal and Factor reversal tests- description. Verification of index numbers satisfying the reversibility tests. Unit and Circular Tests (statements and explanation only). Fisher’s index number is ideal (reasons). Consumer price index numbers: Meaning, uses and brief description of the steps in the construction of a consumer price index number. Construction of consumer price index numbers – Aggregative expenditure method and family budget method.

300 Time Series Analysis

- Explanation of a time series with example, uses of time series analysis. Brief description of the components of a time series with examples. Measurement of trend by Graphical, Semi average, moving averages method (Period of moving average being 3, 4 or 5) and method of least squares applications. Drawing Historigram and plotting trend values.
- Fitting a linear trend- normal equations, obtaining trend values, estimating future trend, drawing the historigram and the trend line. Fitting a second degree (Quadratic) and exponential trends- Normal equations and obtaining the trend equation, making future estimates.

400 Interpolation and Extrapolation

- Binomial expansion method of interpolation and extrapolation- conditions, formula and problems (with two missing values – one within and one outside the range).
- Newton’s method of interpolation and extrapolation, conditions, formula and problems (one missing value-within or outside the range)

500 Theoretical Distributions

- Bernoulli distribution - definition through p.m.f., examples of occurrence of Bernoulli distribution, expressions for mean and variance, features, applications. Bernoulli trials.
- Binomial Distribution- Definition throug p.m.f., examples of occurrence of Binomial distribution, expression for mean and variance, features. Given mean and variance, finding the parameters. Computing probabilities. Recurrence relation between successive probabilities and frequencies. Fitting a Binomial distribution (The case of given p and estimated p), obtaining expected frequencies.
- Poisson distribution - definition through p.m.f., examples of occurrence of Poisson distribution, Expressions for mean and variance, features. Computing probabilities for large n and small p, for the given . Recurrence relation between successive probabilities and frequencies. Finding for given two successive probabilities or frequencies. Fitting a Poisson distribution to the given frequency distribution and finding expected frequencies.
- Hyper-geometric distribution – definition through p.m.f, features and applications.
- Normal distribution - definition through p.d.f., examples of occurrence of Normal distribution, properties, problems on p.d.f and properities. Definition of SNV, standard normal distribution through p.d.f. Finding probabilities and expected numbers when mean and variance are given. Finding the probabilities within one, two and three (sigma) limits. Definitions of Chi-square, Student’s-t distributions through p.d.f. (without explaining the constants), the features of each distribution to be stated

600 Statistical Inference

- a) Descriptions of the terms –population, random sample, simple random sample, parameter, statistic, sample space, parameter space, sampling distribution of a statistic along with examples. Definition of standard error, standard errors for different statistic with examples and its uses.
- Statistical inference: Meaning and branches.
- Estimation: Explanation of the terms - estimation, point estimation and interval estimation, meaning of confidence interval, confidence limits and confidence coefficient with examples.
- Statistical hypothesis: Explanation of the terms - statistical hypothesis, null and alternative hypotheses. Definitions of first and second kind of errors, size of the test, level of significance and power of a test with examples. Critical region and critical value. Description of one – tailed and twotailed tests with examples and diagrams. Definition of null distribution and test statistic.
- b) Large sample tests: Test statistic in case of testing for population mean and equality of means of two populations, population proportion and equality of proportions of two populations. Applications, one tailed and two tailed tests.
- c) Small sample tests: i) t- test: test procedure along with test statistic (one tailed and two tailed). for testing of population mean, equality of means and paired t – test and its applications. ii) Chi square test for testing of population variance, goodness of fit and independence of attributes in a 2x2 contingency table and its applications.

700 Statistical Quality Control

- Meaning of SQC and its uses. Causes of variation – chance and assignable, explanation with examples, meaning of process control and product control with examples, explanation of control chart and control limits; general procedure for drawing control charts (with 3 limits). Construction of and R charts when sample means and ranges of 10 or less samples of sizes 4 or 5 are given. Construction of charts for number of defectives (np or d chart) and number of defects (c-charts) and conclusions.
- Meaning of acceptance sampling and uses. Description of single and double sampling plans, with relative advantages and disadvantages.

800 Operations Research

- a) Meaning of O.R., its definition and scope.
- b) Definition of an LPP – examples, statement of the general linear programming problem. Definition or explanation(as the case may be) of the terms: Objective function, decision variable, non negativity restrictions, solution to an LPP, feasible solution, optimal solution, unique optimal solution, multiple solution, unbounded solution and no solution. Formulation of LPP in case of 2 variables and graphical solutions to the problems. Examples of the cases of unique, multiple, unbounded (max./min.) and no solutions.
- c) Transportation Problem- Statement of T. P., Feasible, basic feasible solution, degenerate solution, non degenerate solution and optimal solution of T. P. Balanced and unbalanced T.P. Finding initial basic feasible solution by North-West Corner Rule and Method of matrix minima (lowest cost entry method). Determine the initial total transportation cost.
- d) Game Theory: Meaning of a competitive game, examples and statement of the characteristics of a competitive game. Explanation of a n-person game, a two – person game, a two – person zero – sum game (a rectangular game), strategy, pure and mixed strategies. Pay off matrix, meaning of maximin and minimax, saddle point; solving a rectangular game with maxmin - minimax principle and dominance principle.
- e) Replacement Theory: Meaning, need for replacement, the principle of replacement in case of items that deteriorate with age (discrete case) without considering the change in money value. The formula for finding the average annual cost and problems relating to it.
- f) Inventory Theory: Meaning of inventory problem, the need for maintaining inventory, advantages and limitations. Explanation of the terms - demand rate, setup cost, holding cost, shortage cost, lead time, stock replenishment, time horizon and economic order quantity (EOQ). Formulae for EOQ, optimum cost, optimum time schedule and frequency of replenishment in the case of uniform demand with no lead time- shortages not allowed and shortages allowed. Computation of EOQ, reorder time, frequency of replenishment, optimum cost, maximum inventory level and maximum shortage level

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