# 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.

## Learning Objectives¶

- 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 Bayesâ€™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

## Measurable Outcomes¶

- 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.

## Pedagogy¶

- Cohort based lecture
- Hands-on projects

## Text & References¶

- Essentials of Probability and Statistics for Engineers and Scientists, by R. Walpole. et al.

## Grading¶

- Class participation: 5%
- Homework: 25%
- Project: 10%
- Mid-term exam: 30%
- Final exam: 30%

## Policies¶

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

## Course Notes¶

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

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