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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

Calculating cumulative density of a binomial

If you flip ten coins that each have a 30% probability of heads, what is the probability at least five are heads?

Instructions

100 XP

  • Answer the above question using the pbinom() function. (Note that you can compute the probability that the number of heads is less than or equal to 4, then take 1 - that probability).

  • Confirm your answer with a simulation of 10,000 trials by finding the number of trials that result in 5 or more heads.