Question: 9.3.8 (Does Nature Prefer Even Numbers?) Generalizing Problem ??, let X be an integer-valued random variable such that X = X I + X2, where

9.3.8 (Does Nature Prefer Even Numbers?) Generalizing Problem ??, let X be an integer-valued random variable such that X = X I + X2, where X I , X2 are independent, identically distributed integer-valued random variables. Show that P { X is even } 2 0.5 (this property has been pointed out to us by Steve MacEachem, personal communication).

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