Consider that we are observing iid copies $(X_i, Y_i)_{i=1}^n$ from random vector $(X, Y)$. According to some historical information, the marginal distributions of $X$ and $Y$ are known, but the joint distribution is unclear. A problem of interest is to estimate $\exp[h(X,Y)]$ for some measurable function $h$. This is of application value. For example, in insurance industry, some life insurance policies will cover both husband and wife . Let $X,Y$ be the left life time of husband and wife after signing the policy and $X, Y$ are usually dependent. The company is able to obtain the marginal distributions of $X$ and $Y$ from historical records. Often, the values of interest are $\min(X, Y)$, $\max(X, Y)$ or their distributions. This paper provides an empirical likelihood estimator to solve this problem. Some nice properties of our estimator are supported by theoretical analysis and simulation results.