Let X1,X2,… be a sequence of independent random variables, uniformly distributed on [0,1]. Define Nn to...

Let X1,X2,… be a sequence of independent random variables, uniformly distributed on [0,1]. Define Nn to be the smallest k such that X1+X2+⋯+Xn exceeds cn=n2+12n−−√, namely,

min{k≥1:X1+X2+⋯+Xk>ck}

Does the limit

limn→∞P(Nn>n)

exist? If yes, enter its numerical value. If not, enter −999.

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milcah answered 9 months ago

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