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Course

Foundations of Probability in R

BasicSkill Level

4.8+

Updated 03/2022

In this course, you'll learn about the concepts of random variables, distributions, and conditioning.

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RProbability & Statistics4 hr13 videos54 Exercises4,350 XP39,750Statement of Accomplishment

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Course Description

Probability is the study of making predictions about random phenomena. In this course, you'll learn about the concepts of random variables, distributions, and conditioning, using the example of coin flips. You'll also gain intuition for how to solve probability problems through random simulation. These principles will help you understand statistical inference and can be applied to draw conclusions from data.

Prerequisites

Introduction to R

1

The binomial distribution

Flipping coins in R

Simulating coin flips

Simulating draws from a binomial

Density and cumulative density

Calculating density of a binomial

Calculating cumulative density of a binomial

Varying the number of trials

Expected value and variance

Calculating the expected value

Calculating the variance

2

Laws of probability

Probability of event A and event B

Solving for probability of A and B

Simulating the probability of A and B

Simulating the probability of A, B, and C

Probability of A or B

Solving for probability of A or B

Simulating probability of A or B

Probability either variable is less than or equal to 4

Multiplying random variables

Expected value of multiplying a random variable

Simulating multiplying a random variable

Variance of a multiplied random variable

Adding two random variables

Solving for the sum of two binomial variables

Simulating adding two binomial variables

Simulating variance of sum of two binomial variables

3

Bayesian statistics

Updating with evidence

Updating with simulation

Updating after 16 heads

Updating with simulation after 16 heads

Prior probability

Updating with priors

Updating with three coins

Bayes' theorem

Updating with Bayes theorem

Updating for other outcomes

More updating with priors

4

Related distributions

The normal distribution

Approximating a binomial to the normal

Simulating from the binomial and the normal

Comparing the cumulative density of the binomial

Comparing the distributions of the normal and binomial for low n

The Poisson distribution

Approximating a binomial with a Poisson

Simulating from a Poisson and a binomial

Density of the Poisson distribution

Sum of two Poisson variables

The geometric distribution

Waiting for first coin flip

Using replicate() for simulation

Simulating from the geometric distribution

Probability of a machine lasting X days

Graphing the probability that a machine still works

Foundations of Probability in R

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Rongjun

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Ethan

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Damian

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Sterling

6 days

Guilherme

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Thashalak

7 days

A must-learn probability course before you step into the world of uncertainty.

Rongjun

Ethan

Sterling

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