Probability via Computation - Week 4

Explore probability concepts through computational methods in this 26-minute video lecture from MIT's 18.S191 Fall 2020 course. Learn how to model epidemic propagation, perform random sampling using rand(), and conduct classic experiments like rolling dice. Dive into Monte Carlo simulations to plot frequencies and understand relative frequency. Examine random variables, uniform random numbers, and visualize pre-generated data. Investigate Bernoulli trials, including the algorithm and probability distribution. Conclude with an illustration of the Central Limit Theorem by flipping many biased coins. Gain practical insights into probability theory through hands-on computational examples.

How to model epidemic propagation?.
Random Sampling using rand().
Classic experiment of Rolling a die.
Monte Carlo Simulation to plot the frequencies.
Relative frequency or proportion of rolls of the die.
Random variables.
Uniform random numbers.
Visualization: plotting the pre-generated data.
Sample events with a given probability: Bernoulli trials.
Algorithm.
What is Bernoulli random variable?.
Probability distribution of random variable.
Flipping many biased coins.
Illustration of Central Limit Theorem.