Discrete equations

· Format:

Discrete ({x_i},{p_i}), i = 1 to n

· Probability mass function:

$\begin{array}{l}\displaystyle f(x_i)=p_i\end{array}$

· Cumulative distribution function:

$\begin{array}{l}\displaystyle F(x)= \displaystyle\sum_{j=1}^i p_j\end{array}$

if $\begin{array}{l}x_i \leq x < x_{i+1}\end{array}$ assuming the x_i"s are in ascending order

· Parameter restrictions:

$\begin{array}{l}\displaystyle p_i \geq 0, n >0, \displaystyle \sum_{i=1}^ n p_i >0\end{array}$

· Domain:

x = {x₁, x₂, ...x_n}

· Mean:

No unique mean

· Mode:

The x_i with the greatest p_i

· Variance:

$\begin{array}{l}\displaystyle \displaystyle\sum_{i=1}^{n} (x_i- \bar{x})^2 p_i\end{array}$

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