Voorbeeld: zalm vangen

Elke herfst vindt de zalmentrek plaats — dan zwemmen zalmen vanuit de oceaan de rivier op om te paaien. Tijdens de tocht terug naar boven (meestal naar de plek waar ze zelf zijn uitgekomen) kunnen de vissen grizzlyberen tegenkomen. Sommige van deze beren kunnen 18 zalmen in 3 uur eten, en bij elke poging om een vis te vangen hebben ze een kans van 0,0333 op succes.

Grizzlyberen die zalmen vangen

We kunnen het vangen van zalm door een grizzlybeer modelleren met een geometrische verdeling.

Voor de volgende oefeningen is het object geom uit scipy.stats alvast voor je ingeladen.

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Basis van kansrekening in Python

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# Getting a salmon on the third attempt
probability = geom.____(k=____, p=____)

# Print the result
print(probability)

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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: Calculating probabilities of two events Exercise 2: Any overlap?Exercise 3: Measuring a sample Exercise 4: Joint probabilities Exercise 5: Deck of cards Exercise 6: Conditional probabilities Exercise 7: Delayed flights Exercise 8: Contingency table Exercise 9: More cards Exercise 10: Total probability law Exercise 11: Formula 1 engines Exercise 12: Voters Exercise 13: Bayes' rule Exercise 14: Conditioning Exercise 15: Factories and parts Exercise 16: Swine flu blood test

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: Normale verdelingen Exercise 2: Bereik van waarden Exercise 3: Normale verdelingen plotten Exercise 4: Binnen drie standaarddeviaties Exercise 5: Normale kansen Exercise 6: Voorbeeld: restaurantbestedingen Exercise 7: Voorbeeld: batterij van een smartphone Exercise 8: Voorbeeld: lengtes van volwassenen Exercise 9: Poissonverdelingen Exercise 10: Voorbeeld geldautomaat Exercise 11: Voorbeeld: ongelukken op de snelweg Exercise 12: Poisson-verdelingen genereren en plotten Exercise 13: Geometrische verdelingen Exercise 14: Voorbeeld: zalm vangen

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Exercise 15: Voorbeeld met vrije worpen Exercise 16: Geometrische verdelingen genereren en plotten

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