In a certain forest, there are 6 couples of bears (couple 1, couple 2, couple 6, each couple contains two distinct bears, a total of 12 distinct bears). They all get together for lunch and are seated randomly around a round table. We say that a certain couple is seated together if the two bears in the couple are seated in adjacent sits. Let X be the number of couples that are seated together, and let X,- be the indicator of the event that the i'th couple is seated together. 1. We want to compute to expected number of couples that are seated together. 1. The probability that the i'th couple is seated together is 2. The expected value E(X5) is 3. The expected value E(X) is 2. We want to nd the variance of the number of couples that are seated together. 1. If U are distinct, then: 1. The probability that the i'th couple and the j'th couple are both seated together is 2. The total number of such pairs iJ is 2. The variance VarlX) is