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+⋯+Xk exceeds cn=n2+n12−−−√ , namely,
Nn = min{k≥1:X1+X2+⋯+Xk>cn}
Does the limit
limn→∞P(Nn>n)
exist? If yes, enter its numerical value. If not, enter −999 .
0.8413
I had the answer 0
is Nn a random variable?
it's Irwin–Hall distribution
Does anyone is sure about their answer?
now i am reconsidering and got phi(1)
p(Nn>n) = P(x1+..xn <cn) = P(Zn<1) central limit