Value-at-Risk Theory and Practice
The first advanced book on value-at-risk
Chapter 3, Page 116 Exercise 10
Use [3.17] to prove that, if the components X1 and X2 of a two-dimensional random vector X are independent, then
E(X1 X2) = E(X1)E(X2)
[3.24]
Solution
Let be the joint PDF of X. Let and be the marginal PDFs of its respective components. By [3.17] and [3.2]:
[s1]
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be the joint PDF
of X. Let
and
be the marginal
PDFs of its respective components. By [3.17] and [3.2]:
