Dobbelsteenworpen optellen

Om de centrale limietstelling te illustreren, gaan we werken met dobbelsteenworpen. We genereren steekproeven en tellen die vervolgens op om het resultaat te plotten.

Je krijgt een functie roll_dice() die de steekproef met dobbelsteenworpen genereert. numpy is al als np geïmporteerd: je moet np.add(sample1, sample2) gebruiken om steekproeven op te tellen. Ook is matplotlib.pyplot als plt geïmporteerd zodat je de histogrammen kunt plotten.

Deze oefening maakt deel uit van de cursus

Basis van kansrekening in Python

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# Configure random generator
np.random.seed(42)

# Generate the sample
sample1 = ____(____)

# Plot the sample
plt.____(____, bins=range(1, 8), width=0.9)
plt.____()

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Deze oefening maakt deel uit van de cursus

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: 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: Van steekproefgemiddelde naar populatiegemiddelde Exercise 2: Een steekproef genereren Exercise 3: De steekproefgemiddelde berekenen Exercise 4: De steekproefgemiddelde plotten Exercise 5: Willekeurige variabelen optellen Exercise 6: Steekproefgemiddelden Exercise 7: Steekproefgemiddelden volgen een normale verdeling Exercise 8: Dobbelsteenworpen optellen

Huidige oefening

Exercise 9: Lineaire regressie Exercise 10: Een model fitten Exercise 11: Toetsscores voorspellen Exercise 12: Residuen onderzoeken Exercise 13: Logistische regressie Exercise 14: Een logistiek model fitten Exercise 15: Voorspellen of studenten slagen Exercise 16: Twee toetsen halen Exercise 17: Afronding