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  3. Foundations of Probability in R
  • 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.

  • 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.

Initializing

Exercise

Updating with simulation after 16 heads

We see 16 out of 20 flips from a coin that is either fair (50% chance of heads) or biased (75% chance of heads). How likely is it that the coin is fair?

Instructions

100 XP
  • Simulate 50,000 cases of flipping 20 coins from a fair coin (50% chance of heads), as well as from a biased coin (75% chance of heads). Save these variables as fair and biased respectively.
  • Find the number of fair coins where exactly 16/20 came up heads, then the number of biased coins where exactly 16/20 came up heads. Save them as fair_16 and biased_16 respectively.
  • Print the fraction of all coins that came up heads 16 times that were fair coins- this is the posterior probability that a coin with 16/20 is fair.