Question: (ii), let X be an integer-valued random variable such that X = X1 + X2, where X1,X2 are independent, identically distributed integer-valued random variables. Show

(ii), let X be an integer-valued random variable such that X = X1 + X2, where X1,X2 are independent, identically distributed integer-valued random variables. Show that P{X is even } ≥ 0.5 (this property has been pointed out to us by Steve MacEachern, personal communication).

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