Independent data

SSU

Random variables $X_1$ and $X_2$ are independent, iff $P[X_1\in I_1,X_2\in I_2]=P[X_1\in I_1]\cdot P[X_2\in I_2]$ for every $I_1$, $I_2$.

This is a mathematical way of saying that one variable doesn’t affect the other.

Equivalent definition

Random variables $X_1$ and $X_2$ are independent, iff $P[X_1\le u_1,X_2\le u_2]=P[X_1\le u_1]\cdot P[X_2\le u_2]$ for every $I_1$, $I_2$.3