De verwachtingswaarde en variantie berekenen

Hoe bereken je de verwachtingswaarde en de variantie van een binomiale verdeling met parameters n=10 en p=0.25?

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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: Laten we een munt opgooien in Python Exercise 2: Munten gooien Exercise 3: Nog meer munten gooien met binom Exercise 4: Kansmassa- en verdelingsfuncties Exercise 5: De kans op defecten voorspellen Exercise 6: Werkstatus voorspellen Exercise 7: Verwachte veroordelingskans bij inbraken Exercise 8: Verwachte waarde, gemiddelde en variantie Exercise 9: De verwachtingswaarde en variantie berekenen

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Exercise 10: De steekproefgemiddelde berekenen Exercise 11: Het resultaat controleren Exercise 12: De steekproefgemiddelde en -variantie berekenen

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: 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