This question is from an example in the book of Bertsekas. (p240 of 1st edition). I would like to know why $$E[X_{i} X_{j}] = P(X_{i} = 1\text{ and }X_{j}=1)$$ and $$E[X_{i}] = P(X_{i}=1)$$. please explain to me. Thanks.
2026-03-28 02:22:13.1774664533
How to calculate E[Xi Xj]?
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$X_iX_j$ takes only two values $0$ and $1$. It is $1$ iff $X_i=X_j=1$. Hence $EX_iX_j$ is $1$ times the probability of $X_i=X_j=1$ plus $0$ times the probability of the complementary event.