Foundations of Probability in R
In this course, you'll learn about the concepts of random variables, distributions, and conditioning.
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Description du cours
Probability is the study of making predictions about random phenomena. In this course, you'll learn about the concepts of random variables, distributions, and conditioning, using the example of coin flips. You'll also gain intuition for how to solve probability problems through random simulation. These principles will help you understand statistical inference and can be applied to draw conclusions from data.
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The binomial distribution
GratuitOne of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.
Flipping coins in R50 xpSimulating coin flips100 xpSimulating draws from a binomial100 xpDensity and cumulative density50 xpCalculating density of a binomial100 xpCalculating cumulative density of a binomial100 xpVarying the number of trials100 xpExpected value and variance50 xpCalculating the expected value100 xpCalculating the variance100 xp - 2
Laws of probability
In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.
Probability of event A and event B50 xpSolving for probability of A and B50 xpSimulating the probability of A and B100 xpSimulating the probability of A, B, and C100 xpProbability of A or B50 xpSolving for probability of A or B50 xpSimulating probability of A or B100 xpProbability either variable is less than or equal to 4100 xpMultiplying random variables50 xpExpected value of multiplying a random variable50 xpSimulating multiplying a random variable100 xpVariance of a multiplied random variable100 xpAdding two random variables50 xpSolving for the sum of two binomial variables50 xpSimulating adding two binomial variables100 xpSimulating variance of sum of two binomial variables100 xp - 3
Bayesian statistics
Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.
Updating with evidence50 xpUpdating50 xpUpdating with simulation100 xpUpdating after 16 heads50 xpUpdating with simulation after 16 heads100 xpPrior probability50 xpUpdating with priors100 xpUpdating with three coins100 xpBayes' theorem50 xpUpdating with Bayes theorem100 xpUpdating for other outcomes100 xpMore updating with priors100 xp - 4
Related distributions
So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.
The normal distribution50 xpApproximating a binomial to the normal50 xpSimulating from the binomial and the normal100 xpComparing the cumulative density of the binomial100 xpComparing the distributions of the normal and binomial for low n100 xpThe Poisson distribution50 xpApproximating a binomial with a Poisson50 xpSimulating from a Poisson and a binomial100 xpDensity of the Poisson distribution100 xpSum of two Poisson variables100 xpThe geometric distribution50 xpWaiting for first coin flip100 xpUsing replicate() for simulation100 xpSimulating from the geometric distribution100 xpProbability of a machine lasting X days100 xpGraphing the probability that a machine still works100 xp
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