Karnataka Public Service Commission, Statistics (Paper I) Papers
About the examination:
Karnataka Public Service commission (KPSC) is said to be one of the most prestigious examinations held in the state of Karnataka for the recruitment of candidates for the state civil services.
Examination pattern:
The examination consists of two rounds. The first one is preliminary examinations, and then comes the mains. In mains, one has to choose two subjects from the given list and both the two subjects have two parts.
About the paper:
Statistics is considered to be one of the important subjects of this examination. The paper deals with various methods and ways of solving problems of different sphere. Topics like probability, analysis, solution through multiple analysis and many more forms the part of this paper.
Syllabus of statistics paper I:
I. Probability:
Sample space and events, probability measure and probability space, Statistical, Independence, Random variable as a measurable function, Discourteous and continuous random variables, Probability density and distribution functions, marginal and conditional distribution functions of random variables and their distributions, expectations and movements, conditional expectation, correlation coefficient; convergence in probability in LP almost everywhere, Markov, Chebychev and Kolmogrov inequalities, Borel Cantelli Lemma, weak and strong law of large numbers probability generating and characteristic functions. Uniqueness and continuity theorems. Determination of distribution by moments. LiderberyDevy Central limit theorem. Standard discrete and continuous probability distributions, their interrelations including limiting cases.
II. Statistical Inference :
Properties of estimates, consistency, unbiasedness, efficiency, sufficiency and completeness. CramerRao bond, Minimum variance unbiased estimation, RaoBlockwell and Lehmann Sheffe’s theorem methods of estimation by moments maximum likelihood, minimum Chisquare. Properties of maximum likelihood estimators confidence intervals for parameters of standard distribution. Simple and composite hypotheses, statistical tests and critical region, two kinds of error, power function unbiased tests, most powerful and uniformly most powerful tests Neyman Person Lemma, optimal tests for simple hypotheses concerning one parameter, monotones likelihood ratio property and its use in constructing UMP tests, likelihood ratio criterion and its asymptotic distribution, Chisquare and Kilmogoro tests for goodness of fit. Run test for randomness Sign test for Location, Wilcoxon MannWhitney test and KologorSmirnov test for the two sample problem. Distribution free confidence intervals for quantities and confidence band for distribution function. Notions of a sequential test, Walds SPRT, its Cc and ASN function.
III. Linear Inference and Multivariate Analysis:
Theory of least squares and Analysis of variance, QaussMarkoff theory, normal equations, least squares estimates and their precision. Tests of significance and Intervals estimates based on least square theory in one way, two ways and three way classified date. Regression Analysis, linear regression, estimates and test about correlation and regression, estimates and tests about correlation and regression coefficient curve linear regression and orthogonal polynomials, test for linearity of regression Multivariate normal distribution, multiple regression, Multiple and partialcorrelation, Mahalanoblis D2 and Hotelling;T2statistics and their applications (derivations of distribution of D2 and T2 excluded) Fisher’s discriminant analysis.
Paper pattern:
The Karnataka Public Service commission statistic paper I is divided into 4 sections. These 4 sections of the paper are named A, B, C and D respectively. Every section has different marking schemes. The first section is of 20 marks only. This section has 4 questions of 5 marks each. The section b is of 100 marks, in which there are all together 10 questions, and every question is of 10 marks. The last two sections are of 90 marks each. However the marking scheme in these sections is different. Section C has all together 6 questions of 15 marks each. Section D has all together 5 questions, and every question is of 30 marks. All the sections are compulsory except for the section D, in which the candidates are asked to answer any three out of the given 5.
Full marks of the question and the time allotted:
The total marks of the paper are 300, and the answers to all the questions are to be written in the time span of 3 hours only.
Download Karnataka Public Service Commission, Statistics (Paper I) Papers
 Download Karnataka Public Service Commission, Statistics (Paper I) Question Paper 1
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