R Probability Distributions

How it works

R distribution families commonly use d for density or mass, p for a cumulative probability, q for a quantile and r for random generation. A binomial model assumes a fixed number of independent trials with a shared success probability. The normal model is continuous and has different support. These are assumptions to justify, not labels automatically inferred from a plot.

Run this R example

These examples run locally with R, not PHP, Python or JavaScript. The reviewed baseline is R 4.5.2 on Windows x64/UCRT, using only packages shipped with R. This is a tested version, not a newest-release claim. Install your own R from the official R project; an IDE is optional. Save the complete source as probability.R in a separate learning folder and run Rscript --vanilla probability.R. Keep code and fictional fixtures separate from a real project.

Bhylu has no R browser runner. There is no Try in playground link because the existing Python and JavaScript editors do not execute R. No package installation, account, network dataset, Apache, MySQL or PHP setting is needed to run these base-R sources.

The complete download uses a local scope, restores its temporary options and treats unexpected warnings as errors. Examples that handle an expected warning do so narrowly. Random examples change only their R process’s RNG state. File examples own their temporary output; figure examples leave their named PNG in the current learning folder and refuse to overwrite it. Use a new empty folder to rerun a figure.

Download the complete probability.R · Download all source files with hash checks

For the optional collection downloader, save download-examples.mjs in an empty folder and run node download-examples.mjs. Local preview before publishing uses node download-examples.mjs http://127.0.0.1:8000/examples/r/. It refuses an existing bhylu-r-examples folder and does not install or execute R.

Example

local({
  previous_options <- options(warn = 2, digits = 8, stringsAsFactors = FALSE)
  on.exit(options(previous_options), add = TRUE)
  cat("binomial mass:", sprintf("%.3f", dbinom(2, size = 4, prob = 0.5)), "\n")
  cat("normal cumulative at zero:", pnorm(0), "\n")
  set.seed(23)
  counts <- rbinom(20, size = 8, prob = 0.25)
  cat("draws:", length(counts), "within support:", all(counts >= 0 & counts <= 8), "\n")
  invisible(NULL)
})

cat("binomial mass:", sprintf("%.3f", dbinom(2, size = 4, prob = 0.5)), "\n")
cat("normal cumulative at zero:", pnorm(0), "\n")
set.seed(23)
counts <- rbinom(20, size = 8, prob = 0.25)
cat("draws:", length(counts), "within support:", all(counts >= 0 & counts <= 8), "\n")

Expected result

binomial mass: 0.375
normal cumulative at zero: 0.5
draws: 20 within support: TRUE

The binomial mass refers to exactly two successes, while pnorm is a cumulative probability up to zero. The random example checks count and support rather than promising exact draws across every future R release. It is not a secure random generator or a real sampling study.