De Morgan's Laws
Lemma 1: \((\bigcup_n S_n)^c=\bigcap_n S_n^c\)
Proof for Lemma 1:
\[\because \forall x \in (\bigcup_n S_n)^c, x \notin \bigcup_n S_n, \therefore x \notin S_i, \forall i \in \{1,2,\...
Law of Iterated Expectations
\(E[Y] = E_X[E[Y |X]].\)
The notation \(E_X[.]\) indicates the expectation over the values of \(X\). Note that \(E[Y|X]\)
is a function of \(X\).
Proof for Law of Itera...