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QUESTION

What is the difference between a discrete uniform distribution and a continuous uniform distribution?

An uniform distibution is a distribution that gives to all its values the same probability to occur.

• Continous case:

the equal probability is given to all the values into an interval [a,b], which contains an infinite number of values. the value of the probability will depend on the range of the interval and will be f(x)=1/(b-a)

• Discrete case:

the equal probability is given to all the values into a specific set S of values which the distibution can have. A clear example of this is the dice: when you throw a dice you have the set S={1,2,3,4,5,6}, and all the numbers have the same probability to occur (unless someone is cheating ;) ) the probability will again depende on the cardinality of S and will be p(x)=1/n.