The Mizoram Public Service Commission is the State Public Service Commission is provided under Article 315 of the Constituion of India to have a Public Service Commission to be consulted by the State Government on the matters of appointment to Civil Services and posts under the Government of Mizoram. Here is a Detailed Syllabus for Mizoram Civil Services Main Exam.
Mizoram Civil Services Examination Syllabus
Optional Paper - Statistics
PAPER – I
PART A
- Sample space and events, probability measure and probability space, random variable as a measurable function, distribution function of a random variable, discrete and continuous-type random variable, probability mass function, probability density function, vector-valued random variable, marginal and conditional distributions, stochastic independence of events and of random variables, expectation and moments of a random variable, conditional expectation, probability generating function, moment generation function, standard discrete and continuous probability distributions.
- Statistical, unbiasedness, consistency, efficiency, sufficiency, completeness, ancillary statistics, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation, Rao-Blackwell and Lehmann-Scheffe theorems, Cramer-Rao inequality for single parameter.
- Estimation by methods of moments, maximum likelihood, least squares, minimum chi-square and modified minimum chi-square, properties of maximum likelihood and other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk function, and minimax estimator. Bayes estimators.
- Non-randomised and randomised tests, critical function, MP tests, NeymanPearson lemma, UMP tests, monotone likelihood ratio, similar and unbiased tests, UMPU tests for single parameter likelihood ratio test and its asymptotic distribution.
- Confidence bounds and its relation with tests.
PART B
- Order Statistics - joint and marginal distribution of order statistics - distribution of range and midrange. Kolmogoroff’s test for goodness of fit and its consistency, sign test and its optimality. Wilcoxon signed-ranks test and its consistency, Kolmogorov-Smirnov two-sample test, run test, Wilcoxon-MannWhitney test and median test.
- Bivariate data: Correlation coefficient and its properties, correlation, correlation ratio, principle of least square, fitting of different curous and fitting of linear regression. Partial and multiple correlation in three variables, their measures and related results. Theory ofr attributes independence and association of attributes. Measure of association for two way classified data
- An outline of fixed-population and super-population approaches, distinctive features of finite population sampling, probability sampling designs, simple random sampling with and without replacement, stratified random sampling, systematic sampling and its efficacy , cluster sampling, two-stage and multistage sampling, ratio and regression methods of estimation involving one or more auxiliary variables, two-phase sampling,
- Fixed effects model (two-way classification) random and mixed effects models (two-way classification with equal observation per cell), CRD, RBD, LSD and their analyses, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial experiments and 22 and 32.
PAPER - II
PART A
- Process and product control, general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and c charts, cumulative sum chart. Single, double, multiple and sequential sampling plans for attributes, OC, ASN, AOQ and ATI curves, concepts of producer’s and consumer’s risks, AQL, LTPD and AOQL, Sampling plans for variables, Use of Dodge-Roming tables.
- Concept of reliability, failure rate and reliability functions, reliability of series and parallel systems and other simple configurations, renewal density and renewal function, Failure models: exponential, Weibull, normal , lognormal. Problems in life testing, censored and truncated experiments for exponential models.
- Different types of models in Operations Research, their construction and general methods of solution, simulation and Monte-Carlo methods formulation of linear programming (LP) problem, simple LP model and its graphical solution, the simplex procedure, the two-phase method and the M-technique with artificial variables, the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems, rectangular games, two-person zero-sum games, methods of solution (graphical and algebraic).
- Replacement of failing or deteriorating items, group and individual replacement policies, concept of scientific inventory management and analytical structure of inventory problems, simple models with deterministic and stochastic demand with and without lead time, storage models with particular reference to dam type. Homogeneous discrete-time Markov chains, transition probability matrix, classification of states and ergodic theorems, homogeneous continuous-time
PART B
- Determination of trend, seasonal and cyclical components, Box-Jenkins method, tests for stationary series, ARIMA models and determination of orders of autoregressive and moving average components, forecasting.
- Commonly used index numbers-Laspeyre’s, Paasche’s and Fisher’s ideal index numbers, chain-base index number, uses and limitations of index numbers, index number of wholesale prices, consumer prices, agricultural production and industrial production, test for index numbers - proportionality, timereversal, factor-reversal and circular .
- Present official statistical system in India relating to population, agriculture, industrial production, trade and prices, methods of collection of official statistics, their reliability and limitations, principal publications containing such statistics, various official agencies responsible for data collection and their main functions.
- Demographic data from census, registration, NSS other surveys, their limitations and uses, definition, construction and uses of vital rates and ratios, measures of fertility, reproduction rates, morbidity rate, standardized death rate, complete and abridged life tables, construction of life tables from vital statistics and census returns, uses of life tables.
- Methods of standardisation of scales and tests, Z -scores, standard scores, Tscores, percentile scores, intelligence quotient and its measurement and uses, validity and reliability of test scores and its determination, use of factor analysis and path analysis in psychometry.
For More Details of Mizoram Public Service CommissionClick Here
