(New page: X~Exp(1) f<sub>X</sub>(x)= k*e^(-k*x) Pr[X>x]= 1-F<sub>X</sub> (x)= e^(-k*x) say we know X>t What is Pr[X>x+t|X>t] We think it is Pr[X>x] Pr[X>x+t|X>t] = Pr[{X>t} {X>x+t}] / Pr[X>t] ...) |
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We think it is Pr[X>x] | We think it is Pr[X>x] | ||
| − | Pr[X>x+t|X>t] = Pr[{X>t} {X>x+t}] / Pr[X>t] = Pr[X>x+t] / Pr[X>t] = e^(-k*(x+t)) / e^(-k*t) = e(-k*t) = Pr[X>x] | + | Pr[X>x+t|X>t] = Pr[{X>t} <math> \cap </math> {X>x+t}] / Pr[X>t] = Pr[X>x+t] / Pr[X>t] = e^(-k*(x+t)) / e^(-k*t) = e(-k*t) = Pr[X>x] |
Revision as of 05:03, 15 October 2008
X~Exp(1)
fX(x)= k*e^(-k*x)
Pr[X>x]= 1-FX (x)= e^(-k*x)
say we know X>t
What is Pr[X>x+t|X>t]
We think it is Pr[X>x]
Pr[X>x+t|X>t] = Pr[{X>t} $ \cap $ {X>x+t}] / Pr[X>t] = Pr[X>x+t] / Pr[X>t] = e^(-k*(x+t)) / e^(-k*t) = e(-k*t) = Pr[X>x]
