Supposeare a sequence of independent random variables withX1,X2,X3,...

on (0, 1). Ifuniform distribution.N = min{n>0 | Xn:n - X1:n>a, 0<a<1 and a is constant}

Xn:n = max Xi, 1 =< i =<n

X1:n = min Xi, 1 =< i =<n.

What is?E[N]

ps. 1)does that sort of stating the problem implies{theorem stating the independence of a complete sufficient statistic and an ancillary statistic}or not?basu theorem

ps. 2)n:n and 1:n are index.