Consider a random variable $Y$ with complex Gaussian distribution, i.e $Y \sim \mathcal{C N}(\mu,\sigma^2)$. We can write $Y$ as real ($Y_r$) and imaginary component ($Y_j$) as $Y = Y_r + i Y_j$. Where, $Y_r \sim \mathcal{N}(\mu,\sigma^2/2)$ and $Y_j \sim \mathcal{N}(0,\sigma^2/2)$.

Now, I am selecting $M$ samples from the $Y$ distribution such that their absolute value ($|Y|$) is bigger than other remaining $N-M$ samples, where $N$ is the total number of samples.

What is the mean and variance of these selected $M$ samples?

Consider a random variable $Y$ with complex Gaussian distribution, i.e $Y \sim \mathcal{C N}(\mu,\sigma^2)$. We can write $Y$ as real ($Y_r$) and imaginary component ($Y_j$) as $Y = Y_r + i Y_j$. Where, $Y_r \sim \mathcal{N}(\mu,\sigma^2/2)$ and $Y_j \sim \mathcal{N}(0,\sigma^2/2)$.

Now, I am selecting $M$ samples from the $Y$ distribution such that their absolute value ($|Y|$) is bigger than other remaining $N-M$ samples, where $N$ is the total number of samples.

What is the mean and variance of these selected $M$ samples? Any bound or asymptotic approach will also work.