Definition$$\PageIndex{1}$$
A random variable $$X$$ has a uniform distribution on interval $$[a, b]$$, write $$X\sim\text{uniform}[a,b]$$, if has pdf given by
$$f(x) =\left\{\begin{array}{l l} \frac{1}{b-a}, & \text{for}\ a\leq x\leq b \\ 0, & \text{otherwise} \end{array}\right.\notag$$
A typical application of the uniform distribution is to model randomly generated numbers. In other words, it provides the probability distribution for a random variable representing a randomly chosen number between numbers $$a$$ and $$b$$.
The uniform distribution assigns equal probabilities to intervals of equal lengths, since it is a constant function, on the interval it is non-zero $$[a, b]$$. This is the continuous analog to equally likely outcomes in the discrete setting.