Random variables $X_{1},X_{2},…,X_{n}$ are **independently and identically distributed** (i.i.d.) if they are all Independent and all have the same distribution.

Warning

By distribution, the parameters must be the same as well. Remember when we talk about something like the Normal distribution, we’re really referring to a

familyof distributions. Therefore, $X∼N(1,4)$ and $Y∼N(1,9)$ would not be i.i.d., even if they both have the Normal distribution, because $σ_{X}=σ_{Y}$.