Rufus Pollock
Useful bits of Maths
The moment-generating function for a random variable $$X$$ is:
$$ \[ M_{X}(t) = E(e^{tX}) \] $$
Useful MGFs:
$$ X \sim N(\mu, \sigma^{2}), M(t) = e^{\mut + 1/2 \sigma^{2} t^{2}} $$
$$ X \sim \textrm{t-distn}, M(t) = \textrm{undefined}, \infty $$
Test Maths
Somthing simple:
$$ x^{2} = 4 $$
Then an eqnarray:
$$ \begin{eqnarray} y & = & x + z \\ & = & x^{2} \end{eqnarray} $$
Then another array setup:
$$ \[ f(x) := \left\{\begin{array}{l l} x^2 \sin \frac1x & \textrm{if } x \ne 0, \\ 0 & \textrm{if } x = 0 . \end{array}\right. \] $$
Testing markdown and markdown maths: $$a$$
$$ x^{2} + 2 = 4
Testing a more complex array setup
$$ \[ f(x) := \left\{\begin{array}{l l} x^2 \sin \frac1x & \textrm{if } x \ne 0, \\ 0 & \textrm{if } x = 0 . \end{array}\right. \] $$
Test Citation Stuff
Bibliography
- [jovanovic_ea_1994]
- Boyan Jovanovic and Glenn M MacDonald. Competitive Diffusion. The Journal of Political Economy, 102(1):24-52, February 1994.
