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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

Comparing the cumulative density of the binomial

If you flip 1000 coins that each have a 20% chance of being heads, what is the probability you would get 190 heads or fewer?

You'll get similar answers if you solve this with the binomial or its normal approximation. In this exercise, you'll solve it both ways, using both simulation and exact calculation.

Instructions

100 XP
  • Use the simulated binom_sample (provided) from the last exercise to estimate the probability of getting 190 or fewer heads.
  • Use the simulated normal_sample to estimate the probability of getting 190 or fewer heads.
  • Calculate the exact probability of the binomial being <= 190 with pbinom().
  • Calculate the exact probability of the normal being <= 190 with pnorm().