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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.
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1
The binomial distribution
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.
- Flipping coins in R50 XP
- Simulating coin flips100 XP
- Simulating draws from a binomial100 XP
- Density and cumulative density50 XP
- Calculating density of a binomial100 XP
- Calculating cumulative density of a binomial100 XP
- Varying the number of trials100 XP
- Expected value and variance50 XP
- Calculating the expected value100 XP
- Calculating the variance100 XP
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.
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.
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.
R
Foundations of Probability in R
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