Question: Let X1, X2, . . . , be independent and identically dis tributed (i.i.d.) continuous random variables with common distribution FX (x) = P{Xi x}.

Let X1, X2, . . . , be independent and identically dis

tributed (i.i.d.) continuous random variables with common distribution FX (x) = P{Xi x}. We

say that a record occurs at time n, n > 0 and has record value Xn if Xn > max{X1, . . . , Xn1},

1where X0 := . Suppose you have generated k such random variables. Find the probability

that the record occurs at time k, i.e., P{Xk > X1, Xk > X2, . . . , Xk > Xk1}.

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