X1 , X2 ... 為 independent identically distributed continuous random variable (獨立,相同,連續,的隨機變數) we say: a record occurs at time n if Xn > max (X1,X2...Xn-1) 即 Xn 比 X1,X2 ...Xn-1 都來的大. show: a) P{a record occurs at time n} = 1/n b) E[number of records by time n] = Σ(1/i) (i=1 ~ n) c) Var(number of records by time n) = Σ(i-1)/(i^2) (i=1 ~ n) d) if N = min{n:n>1 and a record occurs at time n} 證明 E[N] = ∞ 想問一下， 像(b)的 number of records by time n , 那個 by 是 「乘」的意思嗎??? 另外 (b)在求的東西是什麼呢?!? --

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