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Successive offers for my house are independent, identically distributed random variables $X_1, X_2$, ... having density function $f$ and distribution function $F$.

Let $Y_1 = X_1$, let $Y_2$ be the first offer exceeding $Y_1$, and, generally, let $Y_{n+1}$ be the first offer exceeding $Y_n$. Show that $Y_1$, $Y_2$, ... are the arrival times of an inhomogeneous Poisson process. What is the intensity of this Poisson process?

To show it is a poisson process, I am thinking we can show that $Y_n-Y_{n-1}$ which is the inter-arrival time is exponential distributed by showing memoryless. But how should I start... And I am confused by the relationship between $X_n$ and $Y_n$ right now. Please help. Thanks!

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  • $\begingroup$ I think you mean $Y_2$ and $Y_{n+1}$. $\endgroup$ – joriki Dec 6 '19 at 5:59
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    $\begingroup$ Yes! thanks for pointing out $\endgroup$ – TMS Dec 6 '19 at 6:30
  • $\begingroup$ See the solution on page 311-312 here: home.ustc.edu.cn/~zt001062/PTmaterials/… $\endgroup$ – Math1000 Jan 8 at 0:32

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