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  3. Foundations of Probability in Python
  • 1

    Let's start flipping coins

    Free

    A coin flip is the classic example of a random experiment. The possible outcomes are heads or tails. This type of experiment, known as a Bernoulli or binomial trial, allows us to study problems with two possible outcomes, like “yes” or “no” and “vote” or “no vote.” This chapter introduces Bernoulli experiments, binomial distributions to model multiple Bernoulli trials, and probability simulations with the scipy library.

  • 2

    Calculate some probabilities

    In this chapter you'll learn to calculate various kinds of probabilities, such as the probability of the intersection of two events and the sum of probabilities of two events, and to simulate those situations. You'll also learn about conditional probability and how to apply Bayes' rule.

  • 3

    Important probability distributions

    Until now we've been working with binomial distributions, but there are many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial distribution: the normal, Poisson, and geometric distributions.

  • 4

    Probability meets statistics

    No that you know how to calculate probabilities and important properties of probability distributions, we'll introduce two important results: the law of large numbers and the central limit theorem. This will expand your understanding on how the sample mean converges to the population mean as more data is available and how the sum of random variables behaves under certain conditions. We will also explore connections between linear and logistic regressions as applications of probability and statistics in data science.

Initializing

Exercise

Restaurant spending example

Let's go back to the example of the restaurant chain that has been collecting data about customer spending. Recall that the data shows that the spending is approximately normally distributed, with a mean of 3.15 and a standard deviation of 1.5 per customer, as pictured in the plot.

Spending distribution

We can use the already imported norm object from scipy.stats to answer several questions about customer spending at this restaurant chain.

Instructions 1/4

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  • 1

    What is the probability that a customer will spend $3 or less?

  • 2

    What is the probability that a customer will spend more than $5?

  • 3

    What is the probability that a customer will spend more than $2.15 and $4.15 or less?

  • 4

    What is the probability that a customer will spend $2.15 or less or more than $4.15?