Question: Let Y be a random variable with E[Y] < (a) Show that the Mt defined by Mt = E[Y| It] is a martingale. (b)

Let Y be a random variable with
E[Y] < ∞
(a) Show that the Mt defined by
Mt = E[Y| It]
is a martingale.
(b) Does this mean that every conditional expectation is a martingale, given the increasing sequence of information sets {I0 ⊆ · · · ⊆ It ⊆ It+1 ⊆ · · ·}.

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