IITJAM STATISTICS TEST SERIES SCHEDULE 2024 (ONLINE)

Date

TEST TYPE

Modules

Syllabus

MWT01 
Probability Theory 
02Jan24 
Random experiments, sample space and algebra of events, relative frequency and Axiomatic definitions of probability, properties of probability function, addition theorem of probability function (Inclusion –exclusion principle), Geometric probability, Bools and Bonferroni’s inequalities, conditional probability and multiplication rule, theorem of total probability and Baye’s theorem, Pairwise and mutual independent of events.

MWT02 
Integral Calculus 
05Jan24 
Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.

MWT03 
Univariate and standard Distribuion 
08Jan24 
"Definition of random variable cumulative distribution function, discrete & conditions random variables, probability mass function, probability density function, distribution of a function of a random variable using transformation and Jacobian method, mathematical expectation and moments, mean, median mode, variance, standard deviation coefficient of variatioin, Quartiles, measure of skewness and kurtosis of probability distribution. Moment generating function, its properties and uniquess, markov and chebyshev’s inequalities and their application
Degerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeomtric, uniform Experimential double exponential, Gamma, Beta ( I & II type) , normal and Cauchy distributions, their properties, interrelations and limiting (approximation) cases.
"

MWT04 
Multivariate Distribution 
11Jan24 
Marginal c.d.fs of random vector, joint and marginal pmf, joint and marginal pdf, conditional c.d.f., conditional pmf and conditional pdf, independenc of random variables. Distribution of functions of random vector using transformation of variables and Jacobian method, mathematical expectation of functions of random vectors, joint moments, covariance and correlation. Joint moment generating functions and its properties uniquess of joint m.g.f. and its application, conditional moments, condition of expectation and conditional variance, additive properties of binomial, poisson, negative binomial, gamma and normal distribution using their m.g.f..

MWT05 
Real Analysis 
14Jan24 
"Sequences and Series: Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.
Differential Calculus: Limits, continuity and differentiability of functions of one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables."

MWT06 
Standard Multivaitae Limit Theorem and samplimg distrbution 
16Jan24 
Mutlinomial distribution and its properties (moments, correlation, marginal distributions, additive property), Bivariate normal distribution its marginal and conditional distribution and related properties, convergence in probability , convergence in distribution and their interrelations, weak law of large numbers and central limit theorem (iid case) and their applications .Sampling distribution of statistic, definition and distribution of rth order statistic and pdf of iid case for continuous distribution. Distribution of smallest and largest order statistic, Central distribution , Central student’s tdistribution: Snedecor’s central Fdistribution, Relationship between , and distribution.

MWT07 
Estimation 
19Jan24 
Unbiasedness , sufficiency of a statistic, Factorization theorem, complete statistic, consistency and relative efficiency of estimators, uniformly minimum variance unbiased estimator, RaoBlackwell and Lehmann scheffe theorem and their applications, crammer –Rao lower bound, method of moment of maximum likelihood estimator, Invariance of maximum likelihood, estimator least square estimator and its application in simple linear regression modules, confidence intervals and confidence coefficient confidence intervals for the parameters of univariate normal, two independent normal, and exponential distribution.

MWT08 
Linear Algebra 
22Jan24 
Vector spaces with real field, subspaces and sum of subspaces, span of a set. Linear dependence and independence, dimension and basis. Matrices: Rank, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. CayleyHamilton theorem, symmetric, skewsymmetric and orthogonal matrices.

MWT09 
Testing of Hypothesis 
25Jan24 
Null and alternative hypothesis (simple and composite), TypeI and Type –II errors, critical region, level of significance, size and power of the test, Pvalue. Most powerful critical region and tests, Neyman pearson lemma and its application to construction of MP and UMP tests for parameters of single parameter families. Likelihood ratio test for parameters of univariate normal distribution.

FLT01 
Full Length Test 
28Jan24 
As per Exam Pattern 
FLT02 
Full Length Test 
31Jan24 
As per Exam Pattern 
FLT03 
Full Length Test 
04Feb24 
As per Exam Pattern 