Uniform Distribution: Overview, Questions, Preparation

The uniform distribution is a type of probability distribution where all the consequences of an occurrence are likely to be equal in probability theory and statistics. Tossing a coin is an example of uniform distribution. And the likelihood is the same in the coin toss experiment of picking a head or tail. It is possible to divide the uniform distribution into two groups, namely: 
Discrete Uniform Distribution- Each experiment’s outcomes are discrete.

A continuous distribution of odds is a uniform distribution that is synonymous with occurrences that are similarly likely to occur. Two parameters, x and y, are defined, where x = minimum value and y = maximum value. It is commonly denoted as u (x, y).  If a uniform distribution with a continuous random variable X's probability density function or probability distribution is f(b)=1/y-x, then it is denoted by U(x,y), where x and y are constants such that x

Continuous Uniform Distribution- An experiment's result is endless and continuous.

Example of Uniform Distribution

In the table below, the data is 55 times a sedan car honks (in seconds).

Mean sample = 11.49 

The standard deviation for the sample = 6.23. 

The honk times in seconds obey a uniform distribution between 0 and 23 seconds, as assumed (Inclusive). 

Therefore, any honking time is similarly likely to be from 0 to 23.

The theoretical mean = μ = (x+y)/2

μ = (0+23)/2 = 11.50

Standard deviation = √(y−x)2/12

Standard deviation = √(23−0)2/12 =6.64 seconds.

This concept is taught under the chapter Probability. In this, you will learn about the formula and applications of uniform distribution. The weightage of this chapter is 8 marks in the final exam.

1. X on the interval (0,50) is continuously and uniformly distributed. What is the Expected Value (E[x]) and Variance (Var(x)) of X?

Solution. E[x]=a+b/2 and Var(x)=(b−a)2/12

X is uniform on (a,b) 

a is 0 and b is 50  

E[x]=a+b/2=0+50/2=25

Var(x)=(b−a)2/12=2500/12=208.33

Q: What does uniform distribution imply?

Q: What is the shape of a uniform distribution?

Q: What is the difference in distribution between skewed and uniform?

Q: Is there a standard deviation with a uniform distribution?

Q: Why are we increasing the use of uniform distribution?