In joepowers16/rethinking: Statistical Rethinking book package

library(tidyverse)

Probability Distributions

What is a probability distribution? It is just a mathematical function that outputs the probabilities that different outcomes will result from an experiment.

Intuitively, if I have 10 events and a .3 probability of success on each event, then I can form a probability distribution for Binomial(n, p).

(binomial_10_.3 <- dbinom(0:10, 10, .3))

tibble(
  x = as.factor(0:10),
  y = binomial_10_.3
) %>% 
  ggplot(aes(x = x, y = y)) + 
  geom_col()

Intuitively I usally think of a distribution as being the relative frequency of the different outcomes. I often think of this as a histogram, but I can see now that such a histogram could be mathematically described by function like dbinom() when the function inputs the vector of all possible discrete outcomes.

The probability of events in a discrete probability distribution can be described by a probability mass function.

The binomial probability distribution is the discrete probability distribution of the number of successes in n independent trials, each with a binary outcome.

dbinom(
  x = 0:10,  # vector of all possible counts of successful trials
  size = 10, # number of trials (n)
  prob = .3  # probability of success
)

What does this outcome of the binomial distribution

joepowers16/rethinking documentation built on June 2, 2019, 6:52 p.m.