# (Syllabus) RAS Syllabus (Main): Statistics (Code No. 29)

## Rajasthan Public Service Commission

## RAS Syllabus (Main): Statistics (Code No. 29)

## Statistics Paper-I

**1. Probability :**

Classical and Axiomatic definitions of Probability, Addition theorem of
probability, conditional probability, statistical independence and
multiplication theorem of probability, Baye's theorem.

Discret and continuous random variables, probability mass function, probability
density function and cumulative distribution function. Joint, marginal and
conditional distribution of two variables.

Mathematical expectation of functions of one and two random variables, addition
and multiplication theorems on expectation, moments, measure of central
tendency, dispersion, skewness and kurtosis.

Moment generating function and cumulant generating function, characteristic
function and its properties (without proof), variance and covariance of linear
combination of random variable, Chebyshev's inequality, convergence in
probability, weak law of large numbers and simple form of central limit theorem.

**2. Distribution and statistical methods :**

Theoretical probability distribution: Binomial, Poissoan, Negative Binomial,
Hypergeometric, Uniform, Normal, Exponential, Canchy, Laplace, Beta and Gamma
distribution and their inter-relationships. Sampling distribution: concept of
random sample and statistics, its sampling distribution an standard error,
Sampling distribution of X 't', chi-square and 'F' distribution, their
properties and applications in tests of significance. Order statistics and their
sampling distributions in case of uniform and exponential parent distributions.

Theory of attributes, measures of association. Fitting of curve by methods of
least squares, Bivariate frequency distribution, regression, correlation; Karl
Pearson's Kendall's Taurank correlation and intra class correlation
coefficients.

**3. Statistical inference :**

Theory of estimation; criteria of a good estimator; unbiasedness,
consistency, efficiency and sufficiency. Methods of estimation, methods of
moments, maximum likelihood, least square, minimum chi- -square. Cramer Rao
lower bound and minimum variance unbiased estimation and its properties, Best
linear unbiased estimation. Properties of maximum likelihood estimators.
(without proof), Interval estimation, construction of confidence intervals for
parameter of normal distribution only. **Testing of Hypothesis :** Simple and composite hypothesis, statistical
tests, two kinds of errors, best critical region, Neyman-Pearson Lemma and its
application in finding BCR in case of Binomial, Poisson, Uniform, Normal
and exponential populations. Non-parametric methods : Chi-square, sign, median
and run tests. Wilcoxon test rank correlation methods.

## Statistics Paper-II

**1. Sampling Theory :**

Sampling vs complete enumeration, basic principle of sampling. random purposive sampling, Methods of drawing random sample, the principal steps in sample surveys, sampling and non-sampling errors, Simple Random sampling with and without replacement, stratified random sampling, comparison of stratified sampling with SRSWOR, Ratio and regression methods of estimation of population mean and total in large sample size. Comparison with simple estimator, - Systematic sampling, cluster sampling, with equal cluster sizes, Two stage sampling in case of equal sizes in both the stages, Two phase sampling.

**2. Design of Experiments :**

Analysis of variance for one way and two way classification (with on observation per cell), Linear model and its different types, transformation. Basic concepts in design of experiments, criteria for a good design, uniformity trials, size and shape of block and plots., Completely randomized, Randomised block and latin square design. Efficiency of RBD over CRD and LSD over RBD. Factorial experiments, 22 33 and 33 factorial experiments in RBD. Estimation of single missing value in RBD and LSD.

**3. Applied Statistics :**

Index number, various types of index numbers, construction of index number of
prices, fixed base and chain base methods, conversion of fixed base into chain
base and vice versa, uses and limitation of these methods.

Essential requisites or an ideal index, cost of living index number and its
construction, the idea of splicing, base shifting and deflating. Time series and
its components, methods of determining trend and seasonal components. Concept of
Statistical Quality Control. Control charts such as (XR) chart (mean σ) chart, P
chart, np chart c chart, their construction and uses. Sampling inspection by
attributes, single and double sampling inspection plan. O.C. curve, concept of
ASN, AOQ, AOQL, Consumer and producer's risks, PTPD.