- Discrete r.v. $X = \pi(d)$ (defined in another q of mine).
- Discrete r.v. $Y = X - 4.5$.
q1: Would it be incorrect to deduce $Y\sim U(-4.5,4.5)$ from $X\sim U(0,9)$?
q2: If you answered no to q1, please consider this...
- Since $Y$ is a uniformly distributed r.v. centered @ $0$, $E\left[Y\right] = 0$.
If we started sampling $Y$ @ a constant rate (equal to $d$'s incrementation rate), the observed signal would satisfy the definition of "white noise"?