$X,Y$ are independent exponential RV with parameter $\lambda,\mu$. How to calculate
$$ E[\min(X,Y) \mid X>Y+c] $$
probability
asked 2012-12-18
user id:18451
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Two related questions (in the last two days!) : http://math.stackexchange.com/questions/261456/independence-between-maximum-and-minimum-of-exponential/261513 http://math.stackexchange.com/questions/259591/using-the-memoryless-property-to-explain-the-expected-value-of-the-maximum-of-ii/259698 – 2012-12-18
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Do you intend the parameters to be the _rates_, so that the density is $\lambda e^{-\lambda x}$ on $(0,\infty)$, or the expectations, so that the density is $(1/\lambda)e^{-x/\lambda}$ on $(0,\infty)$? Both conventions are sometimes used. – 2012-12-18
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In TeX you should write \min, not \text{min}. Then something like f\min g has proper spacing before and after $\min$, thus $f\min g$. Also, when in a "displayed" rather than "inline" setting, something like \min_{x\in A} looks like this: $\displaystyle\min_{x\in A}$. – 2012-12-18
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@MichaelHardy, the parameters is the rates and thank you for advise in latex~ – 2012-12-19
2 Answers
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[261456] Independence between maximum and minimum of exponential
[259591] Using the Memoryless Property to Explain the Expected Value of the Maximum of iid Exponential RVs