Question: 12. Let X be a random variable which takes values in the interval [M, M] only. Show that P(|X| a) E|X| a

12. Let X be a random variable which takes values in the interval [−M, M] only. Show that P(|X| ≥

a) ≥

E|X| − a M − a if 0 ≤ a < M.

13. Show that Xn →0 in probability if and only if E



|Xn|

1 + |Xn|



→ 0 as n → ∞.

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