# Quantile Regression Expected Value

I know this is probably painfully simple, but can someone help me with the following?

$\textbf{Model:}$

$y=x'\beta(u)$ where $u|x\text{~}Uniform\,[0,1]$ and for any $x,\, x'\beta(\tau)$ is a strictly increasing function in $\tau$.

$\textbf{Question:}$

What is $E[y|x]$

$\textbf{What I Have:}$

I believe the quantile function is: $Q_\tau (y\,|\,x)=x'\beta _\tau$

I know that the quantile function is the inverse CDF, so can I say the following? $$E[y\,|\,x]=\int_{0}^{1}\big(x'\beta _\tau)^{-1}dp$$

I guess my hang-up is: Is $\beta _\tau$ a function of $p$? Or have I misspecified the quantile function

• Where are you getting stuck? How much do you have so far? – Greenparker Mar 17 '16 at 18:10
• @Greenparker I edited the question to include my main hang-up. I appreciate the help! – DornerA Mar 17 '16 at 18:20