MPPSC Statistics Syllabus
The Madhya Pradesh Public Service Commission has published syllabus for the State Services Preliminary Examination 2010 of the MPPSC. The Syllabus of the exam is as follows:

Probability (25 % weight) Random Experiment, sample space, event, algebra of events, classical, Statistical and axiomatic definitions of probability. Basic theorems of probability and simple examples based there on, conditional probability of an event, independent events, Bayes'theorem and its applications. Discrete and continuous random variables and their distributions, expectation, moments, moment generating function. Joint distribution of two random variables, marginal and conditional distributions, independence of random varibles. Discrete Uniform, Binomial, Geometric, Negativebinomial, Hypergeometric, Poission, Uniform, beta, exponential, gamma, Cauchy, normal, and bivariate normal distributions, Chebyshev's inequality. Weak law of large numbers and central limit theorem for independent and identically distributed random variables with finite variance and its simple applications.

Statistical Methods (25 % weight) Concept of a statistical population and a sample, types of data, presentation and summarization of data, measures of central tendency, dispersion, skewness and kurtosis, measures of association and contingency, correlation, rank correlation, correlation ratio, simple and multiple linear regression, multiple and partial correlations (for three variables only). Curvefitting and principle of least squares, concepts of random sample, parameter and statistic. Z and c2 (Chisquare), t and F statistics and their applications.

Statistical Inference (25 % weight) Concept of statistic and its sampling distribution. Point estimate of a parameter. Concept of bias and standard error of an estimate. Standard errors of sample mean and sample proportion. Sampling distrubution (withoutproof) of mean of normal distribution. Independence of sample mean and variance in random sampling from a normal distribution (withoutproof). Statistical Tests and interval Estimation: Null and alternative hypotheses. Types of errors, pvalues. Statement of Chisquare, t, and F. Statistics. Testing for the mean and variance of univariate normal distribution, testing of equality of two means and testing of equality of two variances of two independent univariate normal distributions. Related confidence intervals. Testing for the significance of sample correlation coefficient in sampling from bivariate normal distibution and for the equality of means in sampling from bivariate normal distribution. Large sample tests: Use of central limit theorem for testing and its applications to interval estimation of a single mean, a single proportion, difference of two means and two proportions. Fisher's Ztransformation and its uses. Pearson's Chisquare test for goodness of fit. Contingency table and test of independence in a contingency table Nonparametric tests: Sign test for univariate and bivariate distrbutions, WilcoxonMannWhitney test, Run test, Median test, and Spearman's rank correlation coefficient test.

Sampling theory, Design of Experiments and Quality Control (25 % weight)
Sample Survery, Concepts of population and sample, need for sampling, Census and sample survey, basic concepts in sampling organizational aspects of survey sampling, Sample selection and sample size. Some basic sampling methodssimple random sampling (SRS) with and without replacement. Stratified random sampling. Systematic Sampling. Ratio and regression methods of estimation under SRS. Non sampling errors.
Analysis of varinace for one way and twoway classifications (with one observation per cell). Fundamental principles of design. Basic designsCRD, RBD, LSD and their analysis. Factorial designs2n (n − 4) designs, Main effects and interaction effects and confounding in 23 design (complete confounding)
Concepts of quality and meaning of control. Different types of control charts (X, R, p, np and c). Sampling inspectionsingle and double sampling plans for attributes. OC, ASN and ATI curves Concepts of producer's and consumer's risks.