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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

jovanovic_ea_1994