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Course12710123362 lectures

Engineering Statistics

Prof. Manjesh Hanawal · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 1: Introduction to Probability Video
  2. Lecture 2: Consequences of Axioms Video
  3. Lecture 3: Interpretation of Probability Video
  4. Lecture 4: Total Probability law and Baye’s Theorem I Video
  5. Lecture 5: Total Probability law and Baye’s Theorem II Video

week-02

  1. Lecture 6: Random variables and Cumulative Density Function Video
  2. Lecture 7: Discrete and Continuous random variables I Video
  3. Lecture 8: Discrete and Continuous random variables II Video
  4. Lecture 9: Expectation and Variance Video
  5. Lecture 10: Function of Random variables Video

week-03

  1. Lecture 11: Generating RVs, Joint Distribution of RVs Video
  2. Lecture 12: Joint Distribution of RVs and Marginal densities Video
  3. Lecture 13: Covariance of Random variables Video
  4. Lecture 14: Moment Generating Functions Video
  5. Lecture 15: Conditional PMF and PDF Video

week-04

  1. Lecture 16: Law of Large numbers, Central Limit Theorem Video
  2. Lecture 17: Application of Central Limit Theorem I Video
  3. Lecture 18: Application of Central Limit Theorem II Video
  4. Lecture 19: Gamma and Chisquare distributions Video
  5. Lecture 20: Beta distributions and Exponential families Video

week-05

  1. Lecture 21: Random Sampling, Sample mean and Sample variance Video
  2. Lecture 22: Sampling from Gaussian distribution and t distribution Video
  3. Lecture 23: Student’s t distribution Video
  4. Lecture 24: Fdistribution and its properties Video
  5. Lecture 25: Convergence of Random variables and Consistency Video

week-06

  1. Lecture 26: Order statistics, Median and Percentiles Video
  2. Lecture 27: Generating random sample Direct method Video
  3. Lecture 28: Generating random sample Indirect method Video
  4. Lecture 29: Introduction to python Video
  5. Lecture 30: Python Loops and Numpy library Video

week-07

  1. Lecture 31: Sufficiency Principles and Sufficient Statistics Video
  2. Lecture 32: Sufficient Statistics and Characterizatio n of Sufficient Statistics Video
  3. Lecture 33: Characterizatio n of Sufficient Statistics and Factorization Theorem Video
  4. Lecture 34: Example of Factorization Theorem, Minimal Sufficient Statistics Video
  5. Lecture 35: Minimal sufficient statistics Video

week-08

  1. Lecture 36: Test for minimal sufficient statistics with examples, Ancillary Statistics Video
  2. Lecture 37: Likelihood Functions, Maximum Likelihood Estimator Video
  3. Lecture 38: Method of moments, Baye’s Estimator Video
  4. Lecture 39: Evaluating Estimator, Cramer Rao Bound, Fisher Information Video
  5. Lecture 40: Evaluating Estimator, Cramer Rao Bound, Fisher Information (Contd.) Video

week-09

  1. Lecture 41: Hypothesis Testing, Likelihood Ratio Test Video
  2. Lecture 42: Hypothesis Testing, Bayes Test Video
  3. Lecture 43: Type I and II errors, Power Functions Video
  4. Lecture 44: Type I and II errors, Power Functions (Contd.) Video
  5. Lecture 45: Calculations of Power Functions Video

week-10

  1. Lecture 46: Unbiased Test, Uniformly Most Powerful Test, Neyman Pearson Lemma, Interval Estimation Video
  2. Lecture 47: Interval Estimation Video
  3. Lecture 48: Interval Estimation (Contd.) Video
  4. Lecture 49: Constructiong Confidence Intervals from tests Video
  5. Lecture 50: Python numpy and pandas functions II Video

week-11

  1. Lecture 51: Tutology of tests and confidence intervals Video
  2. Lecture 52: Tutology of tests and confidence intervals (Contd.) Video
  3. Lecture 53: pvalue, ptest of significance of a statistical test Video
  4. Lecture 54: ttest & Ftest, ANOVA Video
  5. Lecture 55: Nonparametric test, Goodness of fit, Chi squared test Video

week-12

  1. Lecture 56: Distribution of Chisquared test statistics Video
  2. Lecture 57: Kolmogrov Smirnov test Video
  3. Lecture 58: Lilliefors’s test and Explorator Data Analysis, QQ Plot and P P Plot Video
  4. Lecture 59: Generating random samples using Python, Hypothesis Testing using Python Video
  5. Lecture 60: Generating random samples using Python, Hypothesis Testing using Python (Contd.) Video

Live Session

  1. Live Session 19-03-2024 Video
  2. Live Session 16-04-2024 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Multidisciplinary
Teacher
Prof. Manjesh Hanawal
Level
Undergraduate
Language
English
Subjects
Mathematics, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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