Unit · year 1
MU-106 · Probability I
Threads chance24 lectures6 theorems
Events, random variables, expectation — reasoning quantitatively about uncertainty.
Lectures
| L01 | Sample Spaces, Events, and the Axioms — |
| L02 | Counting and Equally Likely Outcomes — |
| L03 | Conditional Probability — |
| L04 | Independence — |
| L05 | The Law of Total Probability |
| L06 | Bayes' Theorem |
| L07 | Bayesian Reasoning and Base Rates |
| L08 | Discrete Random Variables and Distributions — |
| L09 | Expectation of a Discrete Random Variable — |
| L10 | Linearity of Expectation |
| L11 | Variance and Standard Deviation — |
| L12 | The Bernoulli and Binomial Distributions — |
| L13 | The Geometric and Poisson Distributions — |
| L14 | Joint Distributions and Independence — |
| L15 | Covariance and Correlation — |
| L16 | Continuous Random Variables and Densities — |
| L17 | The Uniform and Exponential Distributions — |
| L18 | The Normal Distribution — |
| L19 | Transformations of Random Variables — |
| L20 | Markov's Inequality |
| L21 | Chebyshev's Inequality |
| L22 | Modes of Convergence for Random Variables — |
| L23 | The Weak Law of Large Numbers |
| L24 | Synthesis: From Axioms to the Law of Averages |
Theorems in this unit
T-034
The law of total probability
Probability of an event via a partition of the sample space.
T-035
Bayes' theorem
How to invert conditional probabilities.
T-036
Linearity of expectation
Expectation of a sum is the sum of expectations, dependence notwithstanding.
T-037
Markov's inequality
A tail bound from the mean alone for non-negative variables.
T-038
Chebyshev's inequality
A tail bound from the variance.
T-039
The weak law of large numbers
Sample means converge in probability to the expectation.