35. (a) Prove that ????[????] = ????[????|???? < ????]????(???? < ????) + ????[????|???? = ????]????(???? = ????)
Question:
35.
(a) Prove that
????[????] = ????[????|???? < ????]????(???? < ????) + ????[????|???? = ????]????(???? = ????)
HINT: Define an appropriate random variable and then compute ????[????] by conditioning on it.
(b) Use part
(a) to prove Markov’s inequality, which states that if
????(???? = 0) = 1, then for ???? > 0,
????(???? ≥ ????) ≤
????[????]
????
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