Given that the noise current out of a 5Ω resistor is normally distributed with a mean of 0 and a standard deviation of 2 milliamps. Determine the power distribution out of the resistor, $fP(p)$. Determine the mean and standard deviation for the current and the power using Taylor's series. $P = i^2R$.
Edited: More clarification
So the Taylor Series for P would be using the function $P = i^2R$ and the Taylor Series for current would be $I=sqrt(P/R)$?
Let $X \sim \mathcal{N}(0,1)$ then $X^2 \sim \chi^2(1)$ is a chi-square distribution with one degrees of freedom of mean $1$ and variance $2$.
Using the above, for $i \sim \mathcal{N}(0,2)$, then $i^2 \sim \chi^2(1)$ is a chi-square distribution with one degrees of freedom of mean $2$ and variance $8$. Note that
Therefore, $P = i^2 R \sim \chi^2(1)$ is also chi-square with $1$ degrees of freedom, of mean $10$ and variance $8 \times R^2 = 200$ .