Probability Distributions

The binomial distribution models the number of successes in a fixed number of independent trials.

x <- rbinom(100, size=10, prob=0.5)
barplot(table(x), main='Binomial Distribution', col='red')

The Poisson distribution represents the probability of a given number of events occurring in a fixed interval.

x <- rpois(100, lambda=5)
barplot(table(x), main='Poisson Distribution', col='green')

The uniform distribution assigns equal probability to all values within a range.

x <- runif(100, min=0, max=10)
hist(x, main='Uniform Distribution', col='purple')

The exponential distribution describes the time between events in a Poisson process.

x <- rexp(100, rate=1)
hist(x, main='Exponential Distribution', col='orange')

You can generate and compare multiple distributions using plots.

x1 <- rnorm(100, mean=50, sd=10)
x2 <- rnorm(100, mean=60, sd=15)
hist(x1, col=rgb(1,0,0,0.5), main='Comparing Distributions')
hist(x2, col=rgb(0,0,1,0.5), add=TRUE)

You can generate random samples from different distributions for simulations.

set.seed(123)
data <- rnorm(1000, mean=50, sd=10)
hist(data, main='Simulated Normal Distribution', col='blue')

In this lesson, you learned:

• How to generate data from different probability distributions.
• The key characteristics of normal, binomial, Poisson, uniform, and exponential distributions.
• How to compare distributions using histograms.