In an example, I am told that
is $n(0,T)$, i.e., which I took to mean normally distributed with mean of $0$ and variance of $T$.
Note: The value of $b$ and $T$ are unspecified in the problem.
I know the PDF and CDF of the normal and standard normal distributions and I didn't make the pattern recognition. Can you help me see how it is a normal distribution with mean of $0$ and variance of $T$?
Thanks in advance.
Update: Since I am in agreement with Chinny84 and Did that this function does not qualify as being normally distributed, I have chosen to interpret the author's notation as not meaning a normal distribution, but as a simplifying substitution rather than implying a normal distribution - despite the unfortunate use of notation that normally (pun a natural consequence) denotes the normal distribution. And that approach does work (I can't elaborate). The source is a tiny part of a larger problem statement on an exam. I'll award Chinny84 the answer for the help his answer will provide others who come after. Thanks again for your interest/help.