| Line 3: | Line 3: | ||
f<sub>X</sub>(x)= k*e^(-k*x) | f<sub>X</sub>(x)= k*e^(-k*x) | ||
| − | Pr[X>x]= 1-F<sub>X</sub> (x)= e^(-k*x) | + | Pr[ X>x ]= 1-F<sub>X</sub> (x)= e^(-k*x) |
say we know X>t | say we know X>t | ||
| − | What is Pr[X>x+t|X>t] | + | What is Pr[ X>x+t | X>t ] |
| − | We think it is Pr[X>x] | + | We think it is 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] | + | 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 06:05, 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 ]
