How to Rewrite \sum_{i=1}^{n} |(y_i-\theta)|=n\theta in Closed Form?

[member 428835]

$$\sum_{i=1}^{n} |(y_i-\theta)|=n\theta$$

where theta is a fixed constant and $y_i$ is a discrete random variable. does anyone know how to rewrite in close form?? also, everytime i use latex it starts a new line. how can i fix this so i can type directly with my sentances?

thanks

 

[HallsofIvy]

Instead of using "tex" use "itex".

 

[Stephen Tashi]

$$\sum_{i=1}^{n} |(y_i-\theta)|=n\theta$$

where theta is a fixed constant and $y_i$ is a discrete random variable.

It isn't clear what you mean by that equation. Are the $y_i$ random variables that are dependendent on each other in a way that forces $\sum_{i=1}^n |(y_i-\theta)|$ to always add up to be $n \theta$?

Or are you using the notation "|...|" to mean "expected value" instead of "absolute value"?