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| + | [[Category:ECE302Fall2008_ProfSanghavi]] | ||
| + | [[Category:probabilities]] | ||
| + | [[Category:ECE302]] | ||
| + | [[Category:problem solving]] | ||
| + | =Question= | ||
X~Exp(1) | X~Exp(1) | ||
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 ] |
| + | =Answer= | ||
| + | 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] | + | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] |
Latest revision as of 13:19, 22 November 2011
Question
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 ]
Answer
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 ]
