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Foundations of Probability in R

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

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4 Hours13 Videos54 Exercises33,155 Learners

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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.
  1. 1

    The binomial distribution

    Free

    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.

    Play Chapter Now
    Flipping coins in R
    50 xp
    Simulating coin flips
    100 xp
    Simulating draws from a binomial
    100 xp
    Density and cumulative density
    50 xp
    Calculating density of a binomial
    100 xp
    Calculating cumulative density of a binomial
    100 xp
    Varying the number of trials
    100 xp
    Expected value and variance
    50 xp
    Calculating the expected value
    100 xp
    Calculating the variance
    100 xp
  2. 2

    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.

    Play Chapter Now
    Probability of event A and event B
    50 xp
    Solving for probability of A and B
    50 xp
    Simulating the probability of A and B
    100 xp
    Simulating the probability of A, B, and C
    100 xp
    Probability of A or B
    50 xp
    Solving for probability of A or B
    50 xp
    Simulating probability of A or B
    100 xp
    Probability either variable is less than or equal to 4
    100 xp
    Multiplying random variables
    50 xp
    Expected value of multiplying a random variable
    50 xp
    Simulating multiplying a random variable
    100 xp
    Variance of a multiplied random variable
    100 xp
    Adding two random variables
    50 xp
    Solving for the sum of two binomial variables
    50 xp
    Simulating adding two binomial variables
    100 xp
    Simulating variance of sum of two binomial variables
    100 xp
  3. 3

    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.

    Play Chapter Now
    Updating with evidence
    50 xp
    Updating
    50 xp
    Updating with simulation
    100 xp
    Updating after 16 heads
    50 xp
    Updating with simulation after 16 heads
    100 xp
    Prior probability
    50 xp
    Updating with priors
    100 xp
    Updating with three coins
    100 xp
    Bayes' theorem
    50 xp
    Updating with Bayes theorem
    100 xp
    Updating for other outcomes
    100 xp
    More updating with priors
    100 xp
  4. 4

    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.

    Play Chapter Now
    The normal distribution
    50 xp
    Approximating a binomial to the normal
    50 xp
    Simulating from the binomial and the normal
    100 xp
    Comparing the cumulative density of the binomial
    100 xp
    Comparing the distributions of the normal and binomial for low n
    100 xp
    The Poisson distribution
    50 xp
    Approximating a binomial with a Poisson
    50 xp
    Simulating from a Poisson and a binomial
    100 xp
    Density of the Poisson distribution
    100 xp
    Sum of two Poisson variables
    100 xp
    The geometric distribution
    50 xp
    Waiting for first coin flip
    100 xp
    Using replicate() for simulation
    100 xp
    Simulating from the geometric distribution
    100 xp
    Probability of a machine lasting X days
    100 xp
    Graphing the probability that a machine still works
    100 xp

In the following tracks

Statistician with R

Collaborators

Nick Carchedi
Tom Jeon
Nick Solomon

Prerequisites

Introduction to R
David Robinson HeadshotDavid Robinson

Principal Data Scientist at Heap

Dave is the Principal Data Scientist at Heap. He has worked as a data scientist at DataCamp and Stack Overflow, and received his PhD in Quantitative and Computational Biology from Princeton University. Follow him at @drob on Twitter or on his blog, Variance Explained.
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