# Question,

Please provide any simplifications / bounds / concentration results for the expectation of the maximum of two correlated random variables.

$$E\left[\max\left(X,Y\right)\right]=\text{??}$$

$$E\left[\max\left(X,Y\right)\right]\leq\text{??}$$

$$E\left[\max\left(X,Y\right)\right]\geq\text{??}$$

# Assumptions,

We can assume that $X$, $Y$ have a covariance $\sigma_{XY}$ and are from general distribution, $G\left(x\right)$ and $F\left(y\right)$ respectively.

We can assume that the mean, variance and higher moments exist for both the random variables.

# Related Question on the Minimum,

Expectation of Minimum of Two Correlated Random Variables

If there are well known results, please provide references to papers that have detailed steps / derivations.