In the continuous set-up, many times it is observed that the variable follows a specific pattern. This behavior of the r.v. can be described in the mathematical form called probability models, we are going to study a few important continuous probability distributions; such as uniform distribution in excel.
Table of Contents
- What Is Uniform Distribution?
- What is the formula for uniform distribution?
- How do you create a uniform distribution in Excel?
- Uniform Distribution Functions On Excel
- Uniform Distribution On Excel
- FAQ
What Is Uniform Distribution?
In this distribution, the p.d.f. (probability density function) of the random variables remains constant over the range space of the variable.
A continuous-type random variable X is said to follow in distribution over the interval [a, b] if its p.d.f. is given by
f(x) = 1/(b-a) ; a≤x≤b , a< b
What is the formula for uniform distribution?
| Mean | (a+b)/2 |
| Median | (a+b)/2 |
| Variance | (b-a)^2/12 |
| SD | (b-a)/sqrt(12) |
| Kurtosis | -1.2 |
| Skewness | 0 |
How do you create a uniform distribution in Excel?
In order to create a uniform distribution in excel, you need to follow some steps that we are going to share below.
Find out min & max value:- The first step is to find the minimum and maximum from the given question.
Find out the length of the interval:- The second step is to find the length of the interval that can be calculated by subtracting the minimum value from the maximum value.
Find out PDF (Probability Density Function):- Above we are already given you the PDF of Uniform distribution. It is nothing but the ratio of unity and length of the interval.
Find out the Mean:- After calculating the pdf, your next task is to calculate the mean. We have already given the formula to calculate the mean in Uniform Distribution.
Find out the Variance:- After calculating the mean, if it is necessary you can find out the variance by using the formula.
Find out Standard Deviation:- You can calculate the standard deviation, it is nothing but the square root of the variance.
Uniform Distribution Functions On Excel
Excel itself doesn’t provide any special function or formula to calculate the uniform distribution. You need to download the “Real Statistics Resource Pack“, which specially deals with statistics and different types of distribution functions are also given in this pack.
- UNIFORM_DIST(x, α, β, cumulation):- The pdf of the continuous uniform distribution
- UNIFORM_INV(p, α, β):- It is the inverse of the cumulative uniform distribution
Uniform Distribution On Excel
Example: 1 After every 15 minutes there is a bus, If a person arrives at the bus stop, find the probability that the bus will show up in 5 minutes or less.
a=0 \\b=15\\x₁=0\\x₂=5
The probability that the bus shows up in 5 minutes or less is 0.333.
Example 2: The length of an NBA game is uniformly distributed between 130 and 180 minutes. What is the probability that a randomly selected NBA game lasts more than 160 minutes?
a=130 \\b=180\\x₁=160\\x₂=180
The probability that a randomly selected NBA game lasts more than 160 minutes is 0.4.
Example: 3 A random sample of size 10 is taken from a population with a uniform distribution. What is the probability that any random sample element will be less than 6?
FAQ
There are mainly two functions that you can use while performing Uniform distribution in excel. They are Excel RAND and RANDBETWEEN. It helps us to generate pseudo-random numbers.
You can use the RAND function to generate random uniform numbers. You should use =RAND() in any cell to generate these numbers.
This post is all about uniform distribution in excel. It will guide you on your first try. If you find this post helpful then let me know in our comment section.
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