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!