Name for 1 minus Bernoulli variable Consider a Bernoulli variable $X$ with $\Pr[X=1]=p$, $\Pr[X=0]=1-p$. What's a commonly used name for the operation that transforms $X$ into $Y = 1-X$?
Complement (of $X$), inversion are names that come to mind, but I'm not sure what the standard one is, or which will be more easily understood in a technical paper.
To clarify: I'm aware $Y$ is also a Bernoulli variable. I'm asking about the name for the relationship between $X$ and $Y$, or for the operation that transforms $X$ into $Y$.
 A: As @Tim has aleady shown in his answer, if $X$ is a Bernoulli random variable, then so is $Y = 1-X$.
I would call $Y$ the "Complementary Bernoulli random variable" to $X$. I don't know that I've ever heard it called that, or anything else, but if I needed a short and sweet name, that would be it.
Edit: I guess it hasn't caught on, at least exactly as in quotes. Now, 17 months after the post, googling "Complementary Bernoulli random variable" only brings up this post. :(
A: It is still a Bernoulli variable, for example if $Y = 1-X$ where $X \sim \mathrm{Bern}(p)$, then
$$ Y \sim \mathrm{Bern}(1-p) $$
moreover
$$ \Bbb{1}_{Y=0} \sim \mathrm{Bern}(p) $$
where $\Bbb{1}$ is an indicator function, so it is just a matter of labeling the categories. Notice that the labeling is arbitrary since it is always your choice if you code "heads" as $1$, or as $0$; males, or females as $1$ etc., it doesn't matter. 
If you want to name the relationship between the two variables, you can say that $Y$ is $X$ with reversed or switched labels, what led to Bernoulli variable with probability $1-p$.
