(Solved): There are two states of the world, GOOD and BAD where GOOD and BAD are equally likely. If the stat ...

There are two states of the world, GOOD and BAD where GOOD and BAD are equally likely. If the state of the world is BAD then the random variable \( X \) has a value of 3 and the random variable \( Y \) has a value of 15. If the state of the world is GOOD then the random variable \( X \) has a value of 6 and the random variable \( Y \) has a value of 3 . What is the covariance between \( X \) and \( Y \) ? (The formula is on slide 26 in your notes and question \( 2 \mathrm{~b} \) in the practice problem set begins with a covariance calculation (note, however, that here you are asked for the covariance and not the correlation coefficient!). Round your answer to the nearest integer (no decimal places). Do not include a a space, equals sign, space, or any punctuation or text. The Covariance between these two discrete random variables is: \[ \operatorname{Cov}\left(r_{E}, r_{B}\right)=\sum_{s} p(s)\left[r_{E}(s)-E\left(r_{E}\right)\right]\left[r_{B}(s)-E\left(r_{B}\right)\right] \]