So I have a discrete distribution:$$Pr[X=k]=p B(n, a) + (1-p) B(n, b)$$ where $B(n, a)$ and $B(n, b)$ are binomial distributions. I wrote this mixture of distributions from two populations like this:
Let $X\sim B(n, a)$ and let $Y \sim B(n, b)\\$. Then:$$Z \sim p X+(1-p)Y$$ Where Z is my original discrete random variable. Is this notation correct?