Probability and Statistics Questions

Consider a set of independent and identically distributed (i.i.d.) r.v.’s U1, U2, U3, …
s.t. Uı ~ U(0,1). For all k let Sk = k-Ui, and define
Yk = Sk – [Skl,
where [2] is the greatest integer less than or equal to x (notice this defines Yk as
the fractional part of Sk). Show that Yk U(0,1).
Cuestion : Show that the average of the Re’s determined
over an entire cycle of a full period linear congruentiel
generator (LCG) (mod m) is ū =

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