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Date TEST TYPE Modules Syllabus
MWT-01 Probability Theory 02-Jan-24 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.
MWT-02 Integral Calculus 05-Jan-24 Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.
MWT-03 Univariate and standard Distribuion 08-Jan-24 "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. "
MWT-04 Multivariate Distribution 11-Jan-24 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..
MWT-05 Real Analysis 14-Jan-24 "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."
MWT-06 Standard Multivaitae Limit Theorem and samplimg distrbution 16-Jan-24 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 t-distribution: Snedecor’s central F-distribution, Relationship between , and distribution.
MWT-07 Estimation 19-Jan-24 Unbiasedness , sufficiency of a statistic, Factorization theorem, complete statistic, consistency and relative efficiency of estimators, uniformly minimum variance unbiased estimator, Rao-Blackwell 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.
MWT-08 Linear Algebra 22-Jan-24 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. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.
MWT-09 Testing of Hypothesis 25-Jan-24 Null and alternative hypothesis (simple and composite), Type-I and Type –II errors, critical region, level of significance, size and power of the test, P-value. 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.
FLT-01 Full Length Test 28-Jan-24 As per Exam Pattern
FLT-02 Full Length Test 31-Jan-24 As per Exam Pattern
FLT-03 Full Length Test 04-Feb-24 As per Exam Pattern



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