Uniform distribution

The Uniform Distribution is a type of probability distribution in which all outcomes are equally likely. It’s a continuous distribution, meaning that it takes on an uncountable number of possible values. For any given interval within the distribution’s range, the probability is proportional to the length of the interval.

The Uniform Distribution has two parameters:

1. : The minimum value the distribution can take.
2. : The maximum value the distribution can take.

The probability density function of a Uniform Distribution is:

This means that every value between and has the same probability, and this probability is .

The Uniform Distribution is often used in statistics and simulation models where an event has an arbitrary outcome, and all outcomes are equally likely. It’s also often a good assumption to use when there is limited data about a particular event.

Quizzes

Which of the following is an example of uniform distribution in nature?
a) Heights of adult humans
b) Distribution of star positions in a galaxy
c) Distribution of raindrops on a flat surface
d) Weights of fruits in an orchard

Which of the following would indicate a uniform distribution of sales across products in an e-commerce store?
a) A few products have very high sales while others have very low sales
b) All products have roughly the same number of sales
c) Most products have moderate sales with a few outliers
d) Sales vary widely without any discernible pattern

Which of the following is an example of uniform distribution in physics?
a) Distribution of speeds of molecules in a gas at thermal equilibrium
b) Distribution of energy levels in a quantized system
c) Distribution of points in a two-dimensional box
d) Distribution of distances between adjacent particles in a solid

Quizzes with Calculations

If you have a square field of side length 10 meters, and a raindrop can fall anywhere on this field with equal probability, what is the probability that a raindrop falls within a 1 square meter area?

• Solution: The total area of the field is square meters. The area of the region of interest is 1 square meter. Since the distribution is uniform, the probability is the area of the region of interest divided by the total area.
  
• Answer: 0.01

Consider a forest where each of the 100 trees has an equal chance of having a bird nest. If a bird nest is found at a random tree, what is the probability that it is at a specific tree?

• Solution: Since each tree has an equal chance of having a bird nest, and there are 100 trees:
  
• Answer: 0.01

An e-commerce website has 200 products, and each product is equally likely to be sold. What is the probability that a customer buys a specific product?

• Solution: Since each product is equally likely to be sold:
  
• Answer: 0.005