Uniform Probability Distribution
Uniform Probability Distribution
The Uniform Distribution, also known as the rectangular distribution, is a probability distribution where
all outcomes within a specified range are equally likely. It’s like flipping a fair coin or rolling a fair die,
where each outcome has an equal chance of occurring.
Imagine you have a bag of colored balls, and each ball is equally likely to be picked. Let’s say there are
five red balls, five blue balls, and five yellow balls in the bag. If you were to randomly select a ball
without looking, the Uniform Distribution would describe the probability of picking each color. Since
there are an equal number of balls for each color, the chance of picking a red, blue, or yellow ball is 1/3,
or about 33.3%.
Another example of the Uniform Distribution can be seen when choosing a random number from a
given range. Suppose you have a jar containing numbered tickets from 1 to 100, and you randomly pick
a ticket. Each number has the same probability of being selected, so the chance of picking any specific
number is 1/100, or 1%.
Uniform distributions can also be applied to scenarios where events occur randomly within a specific
time or space interval. For instance, imagine you’re observing cars passing by on a road during a specific
hour. If the cars are passing at a constant rate, with an equal chance of any car passing at any given
time, you could model the arrival times using a Uniform Distribution.
The main characteristic of the Uniform Distribution is its constant probability for all outcomes within the
specified range. It represents a situation where no particular outcome is more likely than any other,
making it a simple and intuitive distribution to understand.
The main characteristic of the In summary, the Uniform Distribution describes situations where all outcomes within a given range have an equal probability of occurring. It’s like picking equally likely colored balls from a bag or randomly selecting a number from a range. This distribution is widely used in various fields, including simulations, random number generation, and statistical modeling.
In Python, the scipy.stats module provides functions to work with probability distributions, including the uniform distribution. To compute the probability density function (PDF) or cumulative distribution function (CDF) of a uniform distribution, you can use the following formulas:
In R, the stats package provides functions for working with probability distributions, including the uniform distribution. Here are the formulas to compute the PDF and CDF:
