JAM ACHIEVER COURSE Mathematical Statistics (2022)

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IIT JAM
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This Course is designed and developed by a team of Highly Experienced and Qualified Faculties. It covers entire Syllabus and promise to make Student full prepared to give IIT JAM Exam with confidence.

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  • 1800 Practice Questions & 5 PSPs with Solutions
  • Complete Syllabus Covered
  • Easy to Understand Format
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  • Result Oriented Study Material

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Course Structure

The Curriculum Section of  this Course covers the following Content :

  • 15 Units of Theory
  • 15 Unit wise Practice Question Papers with Solutions (USPs)
  • 5 Volume wise Practice Question Papers with Solutions (VSPs)
  • 10 Full Length Model Solved Papers (MSPs)
  • 5 Previous Year Solved Papers (PSPs)- In Online Mode Only

Module: JAM THEORETICAL COURSE - Mathematical Statistics (MS)

  • Subject: Mathematical Statistics (MS)
    • Section 1: SEQUENCES AND SERIES

        Attachments 1: Introduction

        Attachments 2: Sequence

        Attachments 3: Convergent and Divergent Sequences

        Attachments 4: Bounded and Unbounded Sequence

        Attachments 5: Monotonic Sequence

        Attachments 6: Infinite Series

        Attachments 7: Upper and Lower limits

        Attachments 8: Convergence Criteria for Sequences of Real Numbers

        Attachments 9: Subsequence

        Attachments 10: Cauchy Sequence

        Attachments 11: Absolute and Conditional Convergence

        Attachments 12: Tests of Convergence of Series

        Attachments 13: Convergence of the Infinite Integral

        Attachments 14: Alternating Series

    • Section 2: DIFFERENTIAL CALCULUS-I

        Attachments 1: Introduction

        Attachments 2: Limit of a Function of One Variable

        Attachments 3: Continuous Functions of One Variable

        Attachments 4: Derivability of a Function of One Variable

        Attachments 5: Functions of Two Variables

        Attachments 6: Limit of a Function of Two Variables

        Attachments 7: Continuous Functions of Two Variables

        Attachments 8: Derivability of a Function of Two Variables

    • Section 3: DIFFERENTIAL CALCULUS-II

        Attachments 1: Rolle Theorem : Statement

        Attachments 2: Mean Value Theorem

        Attachments 3: Taylor Theorem

        Attachments 4: Maxima and Minima of One Variable

        Attachments 5: Maxima and Minima of Functions of Two Variables

        Attachments 6: Indeterminate Forms

    • Section 4: INTEGRAL CALCULUS

        Attachments 1: Antiderivatives - Differentiation in Reverse

        Attachments 2: Definite Integrals and Their Properties

        Attachments 3: Differentiation Under the Integral Sign

        Attachments 4: Fundamental Theorem of Calculus

        Attachments 5: Arc Length

        Attachments 6: Double Integral

        Attachments 7: Change of Order of Integration

        Attachments 8: Triple Integrals

        Attachments 9: Surface Area

        Attachments 10: Evaluation of Volumes

    • Section 5: MATRICES

        Attachments 1: Matrices

        Attachments 2: Rank of Matrix

        Attachments 3: Inverse of a Matrix

        Attachments 4: Determinants

        Attachments 5: System of Linear Equations

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

        Attachments 7: Eigen Values and Eigen Vectors

        Attachments 8: Linear Transformation

    • Section 6: DIFFERENTIAL EQUATIONS

        Attachments 1: Introduction

        Attachments 2: Differential Equations

        Attachments 3: Cauchy’s Problem

        Attachments 4: Exact Equation and Its Solution by Insepection

        Attachments 5: Integrating Factors

        Attachments 6: Linear Equation

        Attachments 7: Equation Reducible to Linear form or Bernoulli’s Equation

        Attachments 8: Orthogonal and Oblique Trajectories

        Attachments 9: Homogeneous Differential Equations

        Attachments 10: Cauchy-Euler Equation

        Attachments 11: Linear Equations of Second Order with Variable Coefficients

        Attachments 12: Method of Variation of Parameters

    • Section 7: PROBABILITY

        Attachments 1: Introduction

        Attachments 2: Classical Approach to Probability

        Attachments 3: Axiomatic Approach to Probability

        Attachments 4: Addition Theorems on Probability

        Attachments 5: Conditional Probability

        Attachments 6: Multiplication Theorems on Probability

        Attachments 7: Independent Events

        Attachments 8: The Law of Total Probability

    • Section 8: RANDOM VARIABLES-I

        Attachments 1: Random Variable

        Attachments 2: Distribution Function

        Attachments 3: Discrete Random Variable

        Attachments 4: Continuous Random Variable

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

        Attachments 6: Cumulative Distribution Functions

    • Section 9: RANDOM VARIABLES-II

        Attachments 1: Mathematical Expectation

        Attachments 2: Covariance, Variance of Sums, and Correlations

        Attachments 3: Conditional Expectation

        Attachments 4: The variance and Standard Deviation

        Attachments 5: Moments

        Attachments 6: Moment Generating Functions

        Attachments 7: Characteristic Functions

        Attachments 8: Chebyshev’s Inequality

    • Section 10: STANDARD DISTRIBUTIONS

        Attachments 1: The Bernoulli and Binomial Random Variables

        Attachments 2: The Poisson Random Variable

        Attachments 3: The Negative Binomial Random Variable

        Attachments 4: The Hypergeometric Random Variable

        Attachments 5: The Zeta (or Zipf) Distribution

        Attachments 6: Expectation and Variance of Continuous Random Variables

        Attachments 7: The Uniform Random Variable

        Attachments 8: Normal Random Variables

        Attachments 9: Exponential Random Variables

        Attachments 10: The Gamma Distribution

        Attachments 11: The Weibull Distribution

        Attachments 12: The Cauchy Distribution

        Attachments 13: The Beta Distribution

        Attachments 14: The Normal Approximation to The Binomial Distribution

        Attachments 15: The DeMoivre-Laplace Limit Theorem

    • Section 11: JOINT DISTRIBUTIONS

        Attachments 1: Joint Probability Law

        Attachments 2: Joint Probability Mass Function and Marginal

        Attachments 3: Joint Probability Distribution Function

        Attachments 4: Discrete Distribution Functions

        Attachments 5: Marginal Distribution Function

        Attachments 6: Joint and Marginal Density Functions

        Attachments 7: Conditional Distributions

        Attachments 8: Independent Random Variables

        Attachments 9: Regression

        Attachments 10: Pearson Product-Moment Correlation Coefficient

        Attachments 11: Pearson’s Correlation and Least Squares Regression Analysis

    • Section 12: SAMPLING DISTRIBUTIONS

        Attachments 1: Exact Sampling Distributions (Chi-square Distribution)

        Attachments 2: M.G.F. of Chi-square Distribution

        Attachments 3: Cumulant Generating Function of Chi-square Distribution

        Attachments 4: Limiting Form of Chi-square Distribution for Large Degrees of Freedom

        Attachments 5: Chi-square Probability Curve

        Attachments 6: Chi-square Test of Goodness of Fit

        Attachments 7: Non-central Chi-square Distribution

        Attachments 8: Moment Generating Function of t-Distribution

        Attachments 9: Applications of t-Distribution

        Attachments 10: Non-central t-Distribution

        Attachments 11: F-statistic

        Attachments 12: Mode and Points of Inflexion of F-Distribution

        Attachments 13: Applications of F-Distribution

        Attachments 14: Relation between t and F-Distributions

        Attachments 15: Relation between F and Chi-square

        Attachments 16: Non-Central F-Distribution

    • Section 13: LIMIT THEOREMS

        Attachments 1: Introduction

        Attachments 2: Chebyshev’s Inequality and The Weak Law of Large Numbers

        Attachments 3: The Central Limit Theorem

        Attachments 4: The Strong Law of Large Numbers

    • Section 14: ESTIMATION

        Attachments 1: Introduction

        Attachments 2: Consistency

        Attachments 3: Unbiasedness

        Attachments 4: Efficient Estimators

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

        Attachments 6: Sufficiency

        Attachments 7: Completeness

        Attachments 8: Factorization Theorem

        Attachments 9: Cramer-Rao Inequality

        Attachments 10: Rao-Blackwellisaton

        Attachments 11: Lehmann-Scheffe Theorem

        Attachments 12: Method of Maximum Likelihood Estimation

        Attachments 13: Method of Moments

        Attachments 14: Confidence Interval and Confidence Limits

        Attachments 15: Confidence Intervals for One Parameter Exponential Distributions

    • Section 15: TESTING OF HYPOTHESES

        Attachments 1: Introduction

        Attachments 2: Basic Concepts of Hypothesis Testing

        Attachments 3: Test of Hypothesis about Population Mean

        Attachments 4: Steps in Solving Testing of Hypothesis Problem

        Attachments 5: Most Powerful Test (MP Test)

        Attachments 6: Uniformly Most Powerful Test (UMP Test)

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

        Attachments 8: Likelihood Ratio Tests

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