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R로 배우는 확률 기초

기초기술 수준

업데이트됨 2022. 3.

이 과정에서는 확률변수, 분포, 조건부 확률의 개념을 학습합니다.

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RProbability & Statistics

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확률은 무작위 현상에 대해 예측하는 학문입니다. 이 강의에서는 동전 던지기 예시를 통해 확률변수, 분포, 조건부 개념을 배웁니다. 또한 무작위 시뮬레이션으로 확률 문제를 푸는 직관을 키웁니다. 이 원리는 통계적 추론을 이해하는 데 도움이 되며, 데이터에서 결론을 도출하는 데 적용할 수 있습니다.

선수 조건

Introduction to R

1

The binomial distribution

One 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 R

Simulating coin flips

Simulating draws from a binomial

Density and cumulative density

Calculating density of a binomial

Calculating cumulative density of a binomial

Varying the number of trials

Expected value and variance

Calculating the expected value

Calculating the variance

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 B

Solving for probability of A and B

Simulating the probability of A and B

Simulating the probability of A, B, and C

Probability of A or B

Solving for probability of A or B

Simulating probability of A or B

Probability either variable is less than or equal to 4

Multiplying random variables

Expected value of multiplying a random variable

Simulating multiplying a random variable

Variance of a multiplied random variable

Adding two random variables

Solving for the sum of two binomial variables

Simulating adding two binomial variables

Simulating variance of sum of two binomial variables

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 evidence

Updating with simulation

Updating after 16 heads

Updating with simulation after 16 heads

Prior probability

Updating with priors

Updating with three coins

Bayes' theorem

Updating with Bayes theorem

Updating for other outcomes

More updating with priors

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 distribution

Approximating a binomial to the normal

Simulating from the binomial and the normal

Comparing the cumulative density of the binomial

Comparing the distributions of the normal and binomial for low n

The Poisson distribution

Approximating a binomial with a Poisson

Simulating from a Poisson and a binomial

Density of the Poisson distribution

Sum of two Poisson variables

The geometric distribution

Waiting for first coin flip

Using replicate() for simulation

Simulating from the geometric distribution

Probability of a machine lasting X days

Graphing the probability that a machine still works

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