Uniform Distribution with formula and examples

Definition of Uniform Distribution 

Uniform Distribution is one of the types of Continuous Distribution. A Continuous Random Variable X is said to follow Uniform Distribution with parameter (a,b) if its probability density function (p.d.f) is given by:

f(x) = 1 / (b - a)  , for (a ≤ x ≤ b)

The total probability =

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Mean of Uniform Distribution

The mean of the Uniform Distribution is denoted by  μ or E(X) 

The Variance of Uniform Distribution

The variance of Uniform Distribution is denoted by σ² or V(X).

Uniform Distribution Examples:

Solved Problem 1: The buses on a certain line run every half hour in the day time. What is the probability that a man entering the bus stop after random time during this period will have to wait at least 10 minutes?

= Solution:
Let X be a random variable denoting waiting time in minutes for the next bus.
The interval of waiting is (0, 30) as half hour = 30 minutes.
So the probability density function is given by,

f(x) = 1 / (b-a) = 1 / (30 - 0) = 1/30

The probability that a man entering the bus stop after random time will have to wait at least 10 minutes is. P(X≥10)