
Basic statistical concepts 11
from the joint distribution simply by extracting values of the joint dist
ribu-
tion corresponding to known QoIs and normalizing them by
R
f∈F
p(f, g). This
process is illustrated with Example 1.6.
Example 1.6: Conditional distribution from joint distribution
The concept of the joint probability distribution is illustrated in Figure 1.3. For
clarity, we assum e that f and g are one-dimensional QoIs and for each pair
{g, f} the probability is assigned. We first define all possible true values of
f and g which is the region [0, 1]. An analytical function p(f, g) = 144(f −
0.5)
2
× (g − 0.5)
2
is chosen to represent the joint distribution ...