except, we don't write normal equations like 
. Oh well I guess I'm the one being pedantic now...
We can. For example, if you want to find the expected profit, and you know profit is a function of
, but
is a random variable, then you can write:
)
, and it might be
for example.
I think one reason why they have the lowercase formula is because if you have something like:
)
, you can only change
to
by using the same manipulations on the RHS as well, hence making
For example,
 = \mbox{Pr}\left(\frac{X - \mu}{\sigma} = \frac{0.5 - \mu}{\sigma}\right) = \mbox{Pr}\left(Z = \frac{0.5 - \mu}{\sigma}\right))
Recognise that:
In Methods, we are often using the lowercase formula, but fundamentally, we're using the uppercase formula, which you have to apply to both the LHS and the RHS. I hope you understand the subtle difference, but you really don't need to - most people only superficially understand this (merely changing the
to a
and then using the lowercase formula on the RHS).
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