Let X and Y denote the remaining lifetimes of a husband and wife. Assume that the remaining lifet...
Let X and Y denote the remaining lifetimes of a husband and wife. Assume that the remaining lifetime of each person has an exponential distribution with mean λ and that the remaining lifetimes are independent. An insurance company offers two products to married couples: One which pays when the first spouse dies, that is, at time min(X,Y), and one which pays when the second spouse dies, that is, at time max(X,Y). Calculate the covariance between the two payment timers.
Let X and Y denote the remaining lifetimes of a husband and wife. Assume that the remaining lifetime of each person has an exponential distribution with mean λ and that the remaining lifetimes are independent. An insurance company offers two products to married couples: One which pays when the first spouse dies, that is, at time min(X,Y), and one which pays when the second spouse dies, that is, at time max(X,Y). Calculate the covariance between the two payment timers.