Interactive Course

Foundations of Probability in R

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

4 hours
13 Videos
54 Exercises
12,765 Participants
4,350 XP

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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.

One of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.

Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.

In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.

So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.

1
The binomial distribution
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One of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.
View Chapter Details Play Chapter Now
Laws of probability

In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.
View Chapter Details Play Chapter Now
Bayesian statistics

Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.
View Chapter Details Play Chapter Now
Related distributions

So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.
View Chapter Details Play Chapter Now

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Dave works on the data science behind DataCamp's product and curriculum development. He has worked as a data scientist at Stack Overflow and received his PhD in Quantitative and Computational Biology from Princeton University. His interests include statistics, data analysis, education, and programming in R. Follow him at @drob on Twitter or on his blog, Variance Explained.

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Nick Carchedi
Tom Jeon
Nick Solomon

Prerequisites

Introduction to R

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Foundations of Probability in R

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Course Description

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

Bayesian statistics

Updating with evidence

Updating

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

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

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