The amount of water lost from a dam due to evaporation during a summer is proportional to the dam's surface area. The proportionality factor is random, depending as it does on weather conditions. For a particular reservoir with a particular cross section the surface area increases proportionately to the volume of water in storage. The water in storage during the summer (July and August) is the difference between the water made available since the previous September and the water released since that time. Both these volumes are random. Assume that the water released and the water made available during the summer are negligible. Neglecting second-order effects (e.g., the change in surface area due to the evaporation loss), find the mean and variance of the water lost due to evaporation in a summer in terms of the same moments of the various factors mentioned. Assume a lack of correlation among these factors. Define carefully all the variables, constants, moments, relationships, etc., that you use.