I am currently taking a course from MIT called** Introduction to Probability – The Science of Uncertainty **and this is one of the best courses that I have taken so far. The professor John Tsitsiklis and the other course staffs do great things in this course. How the subjects are studied is quite different than how they are in Turkish education system, hence that makes me realize what our education system lacks: questioning, multiple ways rather than one absolute way to find an answer to a question, developing intuition and application.

Here is some information about content and aim of the course:

### About this course

https://www.edx.org/course/introduction-probability-science-mitx-6-041x-1#!

**Here is my notes:**

**3-Discrete Random Variables:**

-Probability mass functions and expectations

-Variance; Conditioning on an event; Multiple r.v.’s

-Conditioning on a random variable; Independence of r.v.’s

**4-Continuous Random Variables:**

-Probability density functions

-Conditioning on an event; Multiple r.v.’s

-Conditioning on a random variable; Independence; Bayes’ rule

**5- Further topics on random variables**

-Derived distributions

-Sums of r.v.’s; Covariance and correlation

-Conditional expectation and variance revisited; Sum of a random number of r.v.’s

**6- Bayesian inference**

-Introduction to Bayesian inference

-Linear models with normal noise

-Least mean squares (LMS) estimation

-Linear least mean squares (LLMS) estimation

**7- Limit theorems and classical statistics**

-Inequalities, convergence, and the Weak Law of Large Numbers

-The Central Limit Theorem (CLT)

-An introduction to classical statistics

**8- Bernoulli and Poisson processes**

-The Bernoulli process

-The Poisson process

-More on the Poisson process

**9- Markov chains**

-Finite-state Markov chains

-Steady-state behavior of Markov chains

-Absorption probabilities and expected time to absorption