Conditioneren

In veel situaties zijn er gebeurtenissen die afhangen van andere gebeurtenissen, en we willen kansen berekenen met die relaties in het achterhoofd.

Aan de andere kant kun je veel problemen aanpakken door de elementen in je uitkomstenruimte te classificeren. Het is dan makkelijker om te werken met indelingen die geen elementen gemeen hebben — dus die niet overlappen. In deze context: beantwoord de volgende vraag:

Waarom is de regel van Bayes belangrijk?

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Basis van kansrekening in Python

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Basis van kansrekening in Python

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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.

Exercise 1: Let’s flip a coin in Python Exercise 2: Flipping coins Exercise 3: Using binom to flip even more coins Exercise 4: Probability mass and distribution functions Exercise 5: Predicting the probability of defects Exercise 6: Predicting employment status Exercise 7: Predicting burglary conviction rate Exercise 8: Expected value, mean, and variance Exercise 9: Calculating the expected value and variance Exercise 10: Calculating the sample mean Exercise 11: Checking the result Exercise 12: Calculating the mean and variance of a sample

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.

Exercise 1: Kansen van twee gebeurtenissen berekenen Exercise 2: Enige overlap?Exercise 3: Een steekproef meten Exercise 4: Gezamenlijke kansen Exercise 5: Kaartspel Exercise 6: Voorwaardelijke kansen Exercise 7: Vertraagde vluchten Exercise 8: Contingentietabel Exercise 9: Meer kaarten Exercise 10: Wet van de totale waarschijnlijkheid Exercise 11: Formule 1-motoren Exercise 12: Kiezers Exercise 13: Regel van Bayes Exercise 14: Conditioneren

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Exercise 15: Fabrieken en onderdelen Exercise 16: Bloedtest op Mexicaanse griep

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.

Exercise 1: Normal distributions Exercise 2: Range of values Exercise 3: Plotting normal distributions Exercise 4: Within three standard deviations Exercise 5: Normal probabilities Exercise 6: Restaurant spending example Exercise 7: Smartphone battery example Exercise 8: Adults' heights example Exercise 9: Poisson distributions Exercise 10: ATM example Exercise 11: Highway accidents example Exercise 12: Generating and plotting Poisson distributions Exercise 13: Geometric distributions Exercise 14: Catching salmon example Exercise 15: Free throws example Exercise 16: Generating and plotting geometric distributions

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.

Exercise 1: From sample mean to population mean Exercise 2: Generating a sample Exercise 3: Calculating the sample mean Exercise 4: Plotting the sample mean Exercise 5: Adding random variables Exercise 6: Sample means Exercise 7: Sample means follow a normal distribution Exercise 8: Adding dice rolls Exercise 9: Linear regression Exercise 10: Fitting a model Exercise 11: Predicting test scores Exercise 12: Studying residuals Exercise 13: Logistic regression Exercise 14: Fitting a logistic model Exercise 15: Predicting if students will pass Exercise 16: Passing two tests Exercise 17: Wrapping up