# What is the notation for an arbitrary discrete distribution with a specific mean and variance?

Exactly as the title asks. Suppose I have a discrete distribution of which the only thing I know about it is the mean $\mu$ and variance $\sigma^2$. What would be the notation to describe this? Is there something that is commonly used that is similar to the normal distribution?

• Some additional context might lead to more specific advice. Mar 3 '17 at 6:28
• There's not much more really to say. I was just looking for a way to mathematically represent an arbitrary discrete distribution with a known mean and variance instead of explicitly writing out it out. Thanks! Mar 3 '17 at 7:56

Some people write $X\sim F(\mu,\sigma^2)$ (for some unspecified distribution function, $F$) or occasionally $X\sim (\mu,\sigma^2)$ to indicate that $X$ is from some distribution with that mean and variance.
Or you can just say it in words, like "X has a distribution with mean $\mu$ and variance $\sigma^2$"