Question: 7.18 Let Xn be i.i.d. random variables with EX1 = 0 and assume that Xn are bounded. That is, there exists a C > 0

7.18 Let Xn be i.i.d. random variables with EX1 = 0 and assume that Xn are bounded. That is, there exists a C > 0 such that

|X1| ≤ C a.s.

Show that for every ε > 0, P

!

Sn n

≥ ε

"

≤ 2 exp !

(−n

ε2 2c2 )

"

.

Deduce that Sn/n converges in probability to zero.

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