作者homal (\冏/)
看板Statistics
标题[机率] 多个随机变数的问题...
时间Mon Oct 9 16:19:00 2006
X1 , X2 ... 为 independent identically distributed
continuous random variable (独立,相同,连续,的随机变数)
we say: a record occurs at time n
if Xn > max (X1,X2...Xn-1)
即 Xn 比 X1,X2 ...Xn-1 都来的大.
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}
证明 E[N] = ∞
想问一下， 像(b)的 number of records by time n ,
那个 by 是 「乘」的意思吗???
另外 (b)在求的东西是什麽呢?!?
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1F：推 mangogogo:by time n 指的是"到时间n之前" 10/09 20:00