Expected value of multiplication of two indicator random variables?

Question

I found the following statement in a book:

When $k \neq j$ , the variables $X_{ij}$ and $X_{ik}$ are independent, hence

$E[X_{ij}X_{ik}] = E[X_{ij}]E[X_{ik}]$

where E is the expected value. Can anyone explain why this property applies and what would be the affect if $k = j$.

Answer 1

We need to know how the $(X_{ij})$ are defined to answer properly but you must know that for two indépendant variables, the expectation of the product is the product of the expectations.