library(tidyverse)
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
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