Useful Math Formulae
I have written this page because I got sick of
David Powell
asking me questions like "Torst, what's the formula for the sum
of a geometric series?" over and over again. :)
Please note I am using the HTML extensions
<SUP> and <SUB>
for superscript and subscript, as well as some ISO88591
Latin1 characters.
Geometric distribution
 Density: P(Y = n) = p (1  p)^{n  1} for n = 1, 2, ...
 Mean: E(Y) = 1/p
 Variance: Var(Y) = (1p) / p^{2}
Statistics

µ = mean
s = standard deviation
s^{2} = variance

µ = E[X]
µ = (1/N) sum(x)

s^{2}
= E[X  E[X]]^{2}
= E[X  µ]^{2}
= E[X^{2}]  E[X]^{2}
s^{2}
= (1/N)sum(x^{2})  {(1/N) sum(x)}^{2}
s^{2}
= (1/N)sum(x^{2})  µ^{2}
s = sqrt(s^{2})

Let X = { x_{1}, x_{2}, ... , x_{N} }
have mean µ_{x} and variance s_{x}^{2}
Let Y = { y_{1}, y_{2}, ... , y_{N} }
have mean µ_{y} and variance s_{y}^{2}
Let Z = X union Y (Has 2N elements)
Then µ_{z} =
½(µ_{x} + µ_{y})
Then
s_{z}^{2} =
½(s_{x}^{2} + s_{y}^{2}) +
¼(µ_{x}  µ_{y})^{2}
NonLinear Algebra
 max(u,v) = ½(u+v) + ½uv
 min(u,v) = ½(u+v)  ½uv
Arithmetic Series
 Difference: d = t_{n}  t_{n1}
 Term: t_{n} = a + (n1)d
 Sum: S_{n} = ½n(2a + (n1)d)
 Mean: B = (A + C)/2
Geometric Series
 Ratio: r = t_{n} / t_{n1}
 Term: t_{n} = a r^{n1}
 Sum: S_{n} = a (1r^{n}) / (1r)
 Sum to infinity: S_{oo} = a / (1r)
 Mean: B = ± sqrt(AC)
Links