Or, we can start with a function that satisfies the properties of a CDF
for each
x
and then obtain a PDF – in the usual ways for discrete,
continuous, or mixed random variables.
8
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
∙
One sometimes starts with a joint distribution, finds the marginal of
X
, and then obtains
f
Y

X
y

x
using the formula. But in the social
sciences it is much more common to directly specify
f
Y

X
y

x
so that
f
Y

X
.
x
is a PDF for all
x
, often being silent on the distribution of
X
.
The idea is we are interested in how
f
Y

X
.
x
changes with
x
– for
example, how does the earnings distribution change with different
levels of education?
9