Having looked at sequence of decompositions in the last post I can now get some motivation for the definition of a martingale: A sequence of random variables is called a martingale with respect to the decompositions if

## Examples

Let be independent Bernoulli random variables with and and . If show that the sequence is a martingale.

Hence, the sequence of is a martingale. Show that the sequence is also a martingale.

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