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please explain the answers as well 1. Let IA be an indicator random variable for an event A from a sample space . Prove that

please explain the answers as well

1. Let IA be an indicator random variable for an event A from a sample space . Prove that E[IA]=Pr[A]. 2. Let X1 and X2 be random variables (not necessarily independent) over a sample space . Prove that E[X1+X2]=E[X1]+E[X2]

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