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this is an event that again happens with
probability 1/2 because the area under
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probability 1/2 because the area under
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probability 1/2 because the area under
the PDF in this region is equal to 1/2
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the PDF in this region is equal to 1/2
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the PDF in this region is equal to 1/2
so the conditional expectation is a
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so the conditional expectation is a
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so the conditional expectation is a
random variable that takes these values
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random variable that takes these values
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random variable that takes these values
with these probabilities
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with these probabilities
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with these probabilities
since we now have a complete
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since we now have a complete
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since we now have a complete
probabilistic description of this random
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probabilistic description of this random
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probabilistic description of this random
variable we are able to calculate the
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variable we are able to calculate the
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variable we are able to calculate the
expectation of this random variable what
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expectation of this random variable what
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expectation of this random variable what
is it with probability 1/2 the random
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is it with probability 1/2 the random
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is it with probability 1/2 the random
variable takes the value of 1/2 and with
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variable takes the value of 1/2 and with
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variable takes the value of 1/2 and with
probability 1/2
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probability 1/2
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probability 1/2
it takes the value of 2 and so the