JAM ACHIEVER COURSE - Mathematical Statistics (2018)

Joint Admission Test for M.Sc.(IIT JAM)

Complete Comprehensive Course Material

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Course Structure

The Curriculum Section of  this Course covers the following Content :

  • 15 Units of Theory
  • 15 Topic wise Unit Solved Papers (USPs)
  • 5 Volume Solved Papers (VSPs)
  • 10 Full Length Model Solved Papers (MSPs)
  • 4 Previous Year Solved Papers (2014, 2015, 2016, 2017) (PSPs)

Module: JAM THEORETICAL COURSE - Mathematical Statistics

    • Section : Units
      • Unit 1: Sequences and Series

        Lecture 1: Introduction

        Lecture 2: Sequence

        Lecture 3: Convergent and Divergent Sequences

        Lecture 4: Bounded and Unbounded Sequence

        Lecture 5: Monotonic Sequence

        Lecture 6: Infinite Series

        Lecture 7: Upper and Lower limits

        Lecture 8: Convergence Criteria for Sequences of Real Numbers

        Lecture 9: Subsequence

        Lecture 10: Cauchy Sequence

        Lecture 11: Absolute and Conditional Convergence

        Lecture 12: Tests of Convergence of Series

        Lecture 13: Convergence of the Infinite Integral

        Lecture 14: Alternating Series

      • Unit 2: Differential Calculus - I

        Lecture 1: Introduction

        Lecture 2: Limit of a Function of One Variable

        Lecture 3: Continuous Functions of One Variable

        Lecture 4: Derivability of a Function of One Variable

        Lecture 5: Functions of Two Variables

        Lecture 6: Limit of a Function of Two Variables

        Lecture 7: Continuous Functions of Two Variables

        Lecture 8: Derivability of a Function of Two Variables

      • Unit 3: Differential Calculus - II

        Lecture 1: RolleÂ’ Theorem : Statement

        Lecture 2: Mean Value Theorem

        Lecture 3: TaylorÂ’ Theorem

        Lecture 4: Maxima and Minima of One Variable

        Lecture 5: Maxima and Minima of Functions of Two Variables

        Lecture 6: Indeterminate Forms

      • Unit 4: Integral Calculus

        Lecture 1: Antiderivatives - Differentiation in Reverse

        Lecture 2: Definite Integrals and Their Properties

        Lecture 3: Differentiation Under The Integral Sign

        Lecture 4: Fundamental Theorem of Calculus

        Lecture 5: ARC Length

        Lecture 6: Double Integral

        Lecture 7: Change of Order of Integration

        Lecture 8: Triple Integrals

        Lecture 9: Surface Area

        Lecture 10: Evaluation of Volumes

      • Unit 5: Matrices

        Lecture 1: Matrices

        Lecture 2: Rank of Matrix

        Lecture 3: Inverse of a Matrix

        Lecture 4: Determinants

        Lecture 5: System of Linear Equations

        Lecture 6: Consistent and In-Consistent Non-Homogeneous Linear Equations

        Lecture 7: Eigen Values and Eigen Vectors

      • Unit 6: Differential Equations

        Lecture 1: Introduction

        Lecture 2: Differential Equations

        Lecture 3: Cauchy'S Problem

        Lecture 4: Exact Equation and Its Solution by Inspection

        Lecture 5: Integrating Factors

        Lecture 6: Linear Equation

        Lecture 7: Equation Reducible to Linear Form or Bernoulli's Equation

        Lecture 8: Orthogonal and Oblique Trajectories

        Lecture 9: Homogeneous And Non Homogeneous Linear Differential Equations

        Lecture 10: CauchyÂ’-Euler Equation

        Lecture 11: Linear Equations of Second Order with Variable Cofficients

        Lecture 12: Method of Variation of Parameters

      • Unit 7: Probability

        Lecture 1: Introduction

        Lecture 2: Classical Approach to Probability

        Lecture 3: Axiomatic Approach to Probability

        Lecture 4: Addition Theorems on Probability

        Lecture 5: Conditional Probability

        Lecture 6: Multiplication Theorems on Probability

        Lecture 7: Independent Events

        Lecture 8: The Law of Total Probability

        Lecture 9: Baye Rule

      • Unit 8: Random Variable - I

        Lecture 1: Random Variable

        Lecture 2: Distribution Function

        Lecture 3: Discrete Random Variable

        Lecture 4: Continuous Random Variable

        Lecture 5: The Distribution of a Function of a Random Variable

        Lecture 6: Cumulative Distribution Functions

      • Unit 9: Random Variable - II

        Lecture 1: Mathematical Expectation

        Lecture 2: Covariance, Variance of Sums, and Correlations

        Lecture 3: Conditional Expectation

        Lecture 4: The Variance and Standard Deviation

        Lecture 5: Moments

        Lecture 6: Moment Generating Functions

        Lecture 7: Characteristic Functions

        Lecture 8: ChebyshevÂ’ Inequality

      • Unit 10: Standard Distributions

        Lecture 1: The Bernoulli and Binomial Random Variables

        Lecture 2: The Poisson Random Variable

        Lecture 3: The Negative Binomial Random Variable

        Lecture 4: The Hypergeometric Random Variable

        Lecture 5: The Zeta Distribution

        Lecture 6: Expectation and Variance of Continuous Random Variables

        Lecture 7: The Uniform Random Variable

        Lecture 8: Normal Random Variables

        Lecture 9: Exponential Random Variables

        Lecture 10: The Gamma Distribution

        Lecture 11: The Weibull Distribution

        Lecture 12: The Cauchy Distribution

        Lecture 13: The Beta Distribution

        Lecture 14: The Normal Approximation to The Binomial Distribution

        Lecture 15: The DEMoivre-Laplace Limit Theorem

      • Unit 11: Joint Distributions

        Lecture 1: Joint Probability Law

        Lecture 2: Joint Probability Mass Function and Marginal and Conditional Probability Function

        Lecture 3: Joint Probability Distribution Function

        Lecture 4: Discrete Distribution Functions

        Lecture 5: Marginal Distribution Function

        Lecture 6: Joint and Marginal Density Functions

        Lecture 7: Conditional Distributions

        Lecture 8: Independent Random Variables

        Lecture 9: Regression

        Lecture 10: Pearson Product-Moment Correlation Coefficient

        Lecture 11: PearsonÂ’ Correlation and Least Squares Regression Analysis

      • Unit 12: Sampling Distributions

        Lecture 1: Exact Sampling Distributions (Chi-Square Distribution)

        Lecture 2: M.G.F of Chi-Square Distribution

        Lecture 3: Cumulant Generating Function of Chi-square Distribution

        Lecture 4: Limiting Form of Chi-Square Distribution for Large Degrees of Freedom

        Lecture 5: Chi-Square Probability Curve

        Lecture 6: Chi-Square Test of Goodness of Fit

        Lecture 7: Non-Central Chi-Square Distribution

        Lecture 8: Student's 't' Distribution

        Lecture 9: Moment Generating Function of t-Distribution

        Lecture 10: Applications of t-Distribution

        Lecture 11: Non-Central t-Distribution

        Lecture 12: F-Statistic

        Lecture 13: Mode and Points of Inflexion of F-Distribution

        Lecture 14: Applications of F-Distribution

        Lecture 15: Relation Between t and F-Distributions

        Lecture 16: Relation Between F and Chi-Square

        Lecture 17: Non-Central F-Distribution

      • Unit 13: Limit Theorems

        Lecture 1: Introduction

        Lecture 2: ChebyshevÂ’ Inequality and The Weak Law of Large Numbers

        Lecture 3: The Central Limit Theorem

        Lecture 4: The Strong Law of Large Numbers

      • Unit 14: Estimation

        Lecture 1: Introduction

        Lecture 2: Consistency

        Lecture 3: Unbiasedness

        Lecture 4: Efficient Estimators

        Lecture 5: Minimum Variance Unbiased (M.V.U) Estimators

        Lecture 6: Sufficiency

        Lecture 7: Completeness

        Lecture 8: Factorization Theorem

        Lecture 9: Cramer-Rao Inequality

        Lecture 10: Rao-Blackwellisaton

        Lecture 11: Lehmann-Scheffe Theorem

        Lecture 12: Method of Maximum Likelihood Estimation

        Lecture 13: Method of Moments

        Lecture 14: Confidence Interval and Confidence Limits

        Lecture 15: Confidence Intervals for One Parameter Exponential Distributions

      • Unit 15: Testing of Hypotheses

        Lecture 1: Introduction

        Lecture 2: Basic Concepts of Hypothesis Testing

        Lecture 3: Test of Hypothesis about Population Mean

        Lecture 4: Steps in Solving Testing of Hypothesis Problem

        Lecture 5: Most Powerful Test (MP Test)

        Lecture 6: Uniformly Most Powerful Test (UMP Test)

        Lecture 7: Neyman-Pearson Lemma for Testing Simple and Composite Hypotheses

        Lecture 8: Likelihood Ratio Tests

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