1. Let {Y_n: n >0} denote a sequence of i.i.d continuous random variables. A "record" occurs at time nif Y_n= max{Y₁,Y₂,...,Y_n}.
   1. Show that Pr("a "record" occurs at time n") = 1/n
   2. Find the expected number of records by time n= 5
   3. Find the variance of the number of records by time n= 5