Let X1,X2,… be a sequence of independent random variables,uniformly distributed on [0,1]. Define Nn to be the smallest k suchthat X1+X2+?+Xn exceeds cn=n2+12n???, namely,
| Nn | = | min{k?1:X1+X2+?+Xk>ck} | | |
Does the limit
exist? If yes, enter its numerical value. If not, enter?999.
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