📘 MSF

MATHEMATICAL AND STATISTICAL FOUNDATIONS

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MSF Unit 1 Greatest Common Divisors And Prime Factorization And Congruences

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MSF Unit 2 Simple Linear Regression And Correlation

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MSF Unit 3 Continuous Probability Distributions

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MSF Unit 4 Estimation & Tests Of Hypotheses

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MSF Unit 5 Stochastic Processes And Markov Chains

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MSF Mid 1 Quesetion and Answers

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MSF Mid 2 Quesetion and Answers

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Syllabus Overview

UNIT - 1 Greatest Common Divisors and Prime Factorization and Congruences

Greatest Common Divisors and Prime Factorization

  • Greatest common divisors
  • The Euclidean algorithm
  • The fundamental theorem of arithmetic
  • Factorization of integers and the Fermat numbers

Congruences

  • Introduction to congruences
  • Linear congruences
  • The Chinese remainder theorem
  • Systems of linear congruences

UNIT - 2 Simple Linear Regression and Correlation

Simple Linear Regression and Correlation

  • Introduction to Linear Regression
  • The Simple Linear Regression Model
  • Least Squares and the Fitted Model
  • Properties of the Least Squares Estimators
  • Inferences Concerning the Regression Coefficients
  • Prediction
  • Simple Linear Regression Case Study

Random Variables and Probability Distributions

  • Concept of a Random Variable
  • Discrete Probability Distributions
  • Continuous Probability Distributions
  • Statistical Independence
  • Discrete Probability Distributions: Binomial Distribution, Poisson distribution

UNIT - 3 Continuous Probability Distributions

Continuous Probability Distributions

  • Normal Distribution
  • Areas under the Normal Curve
  • Applications of the Normal Distribution
  • Normal Approximation to the Binomial

Fundamental Sampling Distributions

  • Random Sampling
  • Sampling Distributions
  • Sampling Distribution of Means and the Central Limit Theorem
  • Sampling Distribution of S^2
  • t-Distribution
  • F-Distribution

UNIT - 4 Estimation & Tests of Hypotheses

Estimation & Tests of Hypotheses

  • Introduction, Statistical Inference
  • Classical Methods of Estimation
  • Estimating the Mean
  • Standard Error of a Point Estimate
  • Prediction Intervals
  • Tolerance Limits
  • Estimating the Variance
  • Estimating a Proportion for single mean
  • Difference between Two Means
  • Between Two Proportions for Two Samples
  • Maximum Likelihood Estimation

UNIT - 5 Stochastic Processes and Markov Chains

Stochastic Processes and Markov Chains

  • Introduction to Stochastic processes- Markov process
  • Transition Probability
  • Transition Probability Matrix
  • First order and Higher order Markov process
  • N-step transition probabilities
  • Markov chain
  • Steady state condition
  • Markov analysis
MATHEMATICAL AND STATISTICAL FOUNDATIONS Notes