- #1

- 17

- 0

## Homework Statement

[/B]

Calculate [itex]\widehat{Y^{2}}[/itex]

(i.e., the mean of the square of [itex]Y[/itex].

## Homework Equations

[tex]Y=\sum_{k=0}^{N-1}y_{k}[/tex]

where

[tex]y_{k}=e^{-\gamma t}e^{\gamma \tau k}G_{k}[/tex]

and

[tex]t=N\tau[/tex]

The quantities [itex]y_{k}[/itex] (or [itex]G_{k}[/itex]) are statistically independent.

## The Attempt at a Solution

[tex]\widehat{Y^{2}}=\widehat{G^{2}}e^{-2\gamma t}\sum_{k=0}^{N-1}e^{2\gamma \tau k}=\widehat{G^{2}}e^{-2\gamma t}(\ \frac{1-e^{2\gamma t}}{1-e^{2\gamma \tau}} ) [/tex]

However, the correct answer should be

[tex]\widehat{Y^{2}}=\widehat{G^{2}}\frac{1}{2\gamma\tau} (\ 1-e^{-2\gamma \tau} )[/tex]

so it seems like I'm doing something wrong, or is it possible to somehow simplify my answer in order to get the correct one?