The Discrete Uniform Distributions

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Chapter 3
The Discrete Uniform Distributions
? John J Currano, 09/30/2005
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Definition. A random variable, Y, is said to
have a discrete uniform distribution if Y has
finite support, 1, 2, 3,..., n , and
probability function
Examples. 1. n 2 Toss a fair coin.
2. n 6 Toss a fair die. Y the number
showing on the top face.
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Example 2. n 6 Toss a fair die. Y the
number showing on the top face. Find E(Y) and
V(Y).
so
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Theorem. If Y has a discrete uniform
distribution on 1, 2, 3,..., n,, then
a. and b.
The proof of this theorem is a homework problem.
The following summation formulas (which you do
not need to prove) will be useful (1) (2)
These can be proved using mathematical induction.