Foundations of Probability in R
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Learn probability in R through coin flips: binomial and related distributions, laws of probability, and Bayes’ theorem, each checked by simulation.
Probability is about making predictions for random events, and a coin flip is the simplest of them. Using coin flips as the running example, you work with random variables, distributions and conditioning, then check each result by running random simulations in R. That way of thinking supports statistical inference, where conclusions are drawn from data.
What You Will Achieve
- Predict how often a given number of heads turns up across repeated coin flips, and confirm the answer with a simulation in R
- Work out the chance that two events both occur or that at least one occurs, and the expected value of sums and products of random variables
- Apply Bayes’ theorem with a prior to judge whether a coin is fair or biased after seeing its results
- Tell when a normal or Poisson distribution can stand in for a binomial, and estimate how long a machine keeps working
Program Overview
Coin Flips and the Binomial Distribution
Simulating yes/no trials in R and describing how their combined results behave.
- Simulating coin flips and binomial draws
- Density and cumulative density
- Changing the number of trials
- Expected value and variance
Laws of Probability and Bayesian Updating
Combining the probabilities of several events, doing arithmetic with random variables, then updating beliefs about a coin as evidence arrives.
- Probability of A and B, and of A or B
- Multiplying and adding random variables
- Prior probability and updating with evidence
- Bayes’ theorem
Normal, Poisson and Geometric Distributions
Three distributions related to the binomial, when they approximate it, and how to simulate from them.
- Approximating a binomial with the normal
- Approximating a binomial with a Poisson
- Sum of two Poisson variables
- The geometric distribution and how long a machine lasts
Certificate Awarded (Paid)
Job Outlook
Probability reasoning underpins statistical inference, so these skills are used wherever conclusions are drawn from data, including analysis work carried out in R.
Good for: R users who want a working grasp of probability, with every rule checked by a simulation they write themselves.
Keep in mind: Nearly every example is built on coin flips, with a machine lifetime problem in the last chapter as the main exception, so the ideas are met through simple random trials.
Bottom line: Pairing each formula with an R simulation gives a practical way into probability rules, Bayes’ theorem and the binomial, normal, Poisson and geometric distributions.
Frequently Asked Questions
How are simulations used throughout the lessons?
Each chapter pairs a calculation with a random simulation in R: you work out a probability or expected value, then generate random draws to see whether the simulated result agrees. The geometric distribution lessons also use the replicate() function to repeat a simulation many times.
What problem does the Bayesian chapter work through?
It asks whether a coin is fair or biased. You update that belief after seeing results such as 16 heads, bring in prior probabilities, extend the problem to three coins, and then reach the same answers through Bayes' theorem and through simulation.
How do the normal, Poisson and geometric distributions connect to the binomial?
The last chapter shows when a normal or a Poisson distribution can approximate a binomial, with simulations comparing them and a look at the normal and binomial for a small number of trials. The geometric distribution models the wait before a coin flip result first appears and is applied to how long a machine keeps working.
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