Re: [機統] 一題交大統計所的考題
※ 引述《suspect1 ()》之銘言：
: Random Variable X have a uniform distribution in the union of intervals
: (0,a) and (a+2,b)。 F 是X的cdf。若F(4)=0.2，F(a+1) = 0.25 試求 a 和 b
: sol: a=5, b=22
The length of union of intervals is [a-0]+[b-(a+2)] = b-2
X ～ f(x) = 1/(b-2) 0<x<a, a+2<x<b
F(4) < F(a+1) = F(a) → a>4
^^^^^^^^^^^^^
[a,(a+2)] is gap of domain of the random varaible
F(4) = 0.2 → ∫_{0,4} 1/(b-2) dx = 0.2 → b=22
F(a+1) = F(a) = 0.25 → ∫_{0,a} 1/(22-2) dx = 0.25 → a=5
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