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Discrete Uniform Random Distribution

Why is the matlab command called unidrnd?

It come from the notion of a special type of distribution function m which assigns the same mass to all outcomes, then because the distribution function sums to one, each mass must be

\begin{displaymath}m(\omega_i)=\frac{1}{\vert\Omega\vert},\qquab \mbox{ for all } \omega_i \in \Omega\end{displaymath}


Example: Pick at ``random'' among 100 people, means pick giving everyone an equal chance of being picked. Each person is equally likely to be chosen. Implicit in many every day use of random is the fact that the draw should be fair or unbiased.

If $\Omega$ is the outcome space and A some event:

Property 1: If all outcomes in a set $\Omega$ are equally likely the probability of the event is the number of outcomes in A over the number of outcomes in $\Omega$.

\begin{displaymath}P(A)=\frac{\char93 A}{\char93  \Omega}\end{displaymath}

Example
Suppose the experiment is to draw a random number between 1 and 100, each with the same probability, draw uniformly at random.

\begin{displaymath}\Omega=\{1,2,3,4,5,6,\ldots,98,99,100 \}\end{displaymath}

$\char93 \Omega=100$, and $m(3)=m(7)=\cdots=.01$.


next up previous index
Next: Computer Simulation Up: Sample Space 09/24 Previous: Definition of Probability 9/25
Susan Holmes
1998-12-07