Again consider the die example of Problem 2.3. Show that the property holds for A being the

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Again consider the die example of Problem 2.3. Show that the property 

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holds for A being the event of throwing an even number.

Problem 2.3.

Consider rolling a fair die, with X(ω) as the number of pips and the event A of throwing an even number. Show that the conditional expectation, given A, is greater than the unconditional expectation.

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