30.003 Introduction to Probability and Statistics¶

No. of Credits: 12 Subject Credits

Pre-requisites:

Goal¶

The aim of this course is to introduce concepts of Probability and Statistics.

Apply key concepts of probability, including discrete and continuous random variables, probability distributions, conditioning, independence, expectations, and moments
Define and explain the different statistical distributions (e.g., normal, log-normal, Poisson) and the typical phenomena that each distribution often describes
Apply the basic rules and theorems in probability including Bayes’s theorem and the Central Limit Theorem (CLT)
Define and demonstrate the concepts of estimation and properties of estimators
Apply the concepts of interval estimation and confidence intervals
Apply the concepts of hypothesis testing and p-value
Apply the method of least squares to estimate the parameters in a regression model
Use software to facilitate statistical analysis

Evaluate the probabilities and conditional probabilities
Evaluate expectations and conditional expectations of random variables
Approximate the distribution of sum of random variables using CLT
Construct point estimators using the method of maximum likelihood
Calculate the number of samples needed to construct confidence levels on the mean and variance of a normal distribution
Design hypothesis tests for a given set of data and select the appropriate thresholds for the tests
Use linear regression analysis to develop an empirical model of experimental data.
Apply computer programs to facilitate the analysis of data.

Homework is assigned on every week and is due in the 1^st class of the following week.

This set of course notes was graciously shared by Wei Min Cher , updated as of 05 January 2020.