Malini Arvind

@malini

active 2 weeks, 5 days ago
https://www.youtube.com/playlist?list=PLUl4u3cNGP60uVBMaoNERc6knT_MgPKS0 https://www.youtube.com/playlist?list=PLUl4u3cNGP60hI9ATjSFgLZpbNJ7myAg6 1. Conditional probability: given couple has 2 children and one is boy, probability of having girls. (Answer depends on prior assumptions: have child till first boy, 2 children in total, have child […] View
  • Malini Arvind posted an update 2 weeks, 6 days ago



    1. Conditional probability:
    given couple has 2 children and one is boy, probability of having girls. (Answer depends on prior assumptions: have child till first boy, 2 children in total, have child till first girl, etc)

    2. Total probability law

    3. Bayes rule:
    Probability it’s raining given answers of 3 friends having 1/3 probability of lying

    4. Probability densities:
    CDFs, PMFs, PDFs, joint vs marginal vs conditional distribution

    5. Expectations –
    Basics
    optimize a random number generator which is rerun if 1st throw is less than 0.5

    6. Variance

    7. Moments

    8. Stochastic processes:
    Bernoulli, Binomial, geometric, exponential, poisson, Erlang
    – estimate/describe bias of coins given 10 throws
    – estimate accidents in a city given prior daily data

    9. Distributions:
    Gaussian

    10. Markov Chains:
    birth death/pagerank/gambler’s ruin
    Steady state probabilities, absorption probabilities, periodicity, state classes (recurrent/transient)
    – estimate queue size in a shopping mall with appropriate assumptions
    – estimate number of phone lines for a city

    11. Descriptive statistics

    12. Law of large numbers and Central Limit Theorem
    Convergence in probability & distribution

    13. Confidence Intervals

    14. Bayesian Inference: LMS, LLMS
    – trajectory estimation
    – device measurement error accommodation

    15. Estimator Error equation in terms of Bias vs variance tradeoff

    16. Statistical Inference:
    Maximum Likelihood Estimator: derivation from likelihood vs KL divergence

    17. Method of moments
    18. Fischer Information: formulation and interpretation
    mutidimensional gradients and Hessian

    19. Goodness of Fit
    (Todo) ANOVA

    20. Statistical Tests
    t-tests

    21. Hypothesis Testing

    22. Regression and Generalized Linear Models

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