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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

Adults' heights example

The heights of adults aged between 18 and 35 years are normally distributed. For males, the mean height is 70 inches with a standard deviation of 4. Adult females have a mean height of 65 inches with a standard deviation of 3.5. You can see how the heights are distributed in this plot:

Adults heights distribution for male and female

Using the previous information, complete the following exercises.

For your convenience, norm has been imported from the library scipy.stats.

Instructions 1/4

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  • 1

    Print the range of female heights one standard deviation from the mean.

  • 2

    Print the value where the tallest males fall with 0.01 probability.

  • 3

    Print the probability of being taller than 73 inches for a male and for a female.

  • 4

    Print the probability of being shorter than 61 inches for a male and for a female.