Let remaining life of couple of husband and wife is independent and uniformly distributed over $[0,40]$. The insurance company offers 2 products for married couples, namely the first payment when the husband dies and the second when the husband and wife die. Calculate the covariance of the two payments.
I have tried as below.
Let $X$ and $Y$ be remaining life of husband and wife respectively, so we have $$ f(x,y)= \begin{cases} \dfrac{1}{1600}& 0\leq x\leq 1, 0\leq y\leq 1\\ 0&\text {otherwise} \end{cases}. $$
Now I confused to determine the mathematics language of "the covariance of the two payments". Is it right we are asked to compute $\operatorname{cov}(40-X,40-X-Y)$?