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