Hi buddy here I have come to get Bihar Public Service Commission (BPSC) mains exam syllabus of Statistics paper , so would you plz provide me same ??

As you are looking for Bihar Public Service Commission (BPSC) mains exam syllabus of Statistics paper, so on your demand I am providing same for you :

I.
Probability—Sample
space and events, probability measures and •
probability space. Statistical independence, Random variable as a mesurable
function, Discrete and continuous randon variables. Probability density and
distribution functions, marginal and conditional distributions functions of
random variables and their distribution, expectation and movements,
conditional expectation correlation co-efficient; convergence in probability in
LP almost everywhere; Markov, Chebychev and Kolmogrov inequalities.
Borel—Cantellilemma, Weak and strong law of large numbers probability
generating and characteristic functions. Uniqueness and continuity theorems.
Determination of distribution by moments Lindeberg-Levy Centrel limit
theorem. Standard discrete and continuous probability distribution, their
interrelations including limiting cases.
II.
Statistical Inference—Properties
of estimates, consistency,
unbiasedness, efficiency, sufficiency and completeness Cromer-Rao bond,
Minimum variance unbiassed estimation, Rao Blockwell and Lehinann Sheffe's
theorem methods of estimation by moments maximum likelihood, minimum
Chi-square. Properties of maximum likelihood estimators confidence intervals
for parameters of standards distribution.
Simple and composite hypothesis, statistical tests and critical region,
two kinds of error, power function unbiased tests, most powerful and
uniformaly most powerful tests Neyman person Lemma, Optimal tests for
simple hypotheses concerning, one parameter, monotone likelihood ratio
property and its use in constructing UMP test, likelihood ratio criterion and
its asymptotic distribution, Chi-square and. Kolmogoro tests fox goodness of
fit. Run test for randomness. Sign test for Location. Wilcoxon-Mann-whitney
test and Kologor-Simirnov test for the two sample problem. Distribution free
confidence intervals for quantities and corifidence bands for distribution
functions. 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, Gausse Markoff theory, normal equations, least
square estimates and their precision. Tests of significance and intervals
estimates based on least square theory in one
way, two way and three way
classified data. Regression Analysis, linear 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 partial correlation.

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