Let V denote rainfall volume and W denote runoff volume (both in mm). According to the article "Runoff Quality Analysis of Urban Catchments with Analytical Probability Models" (J. of Water Resource Planning and Management, 2006: 4-14), the runoff volume will constant) is the runoff coefficient. The cited article proposes an exponential distribution with parameter l for V.
a. Obtain an expression for the cdf of W. [Note: W is neither purely continuous nor purely discrete; instead it has a "mixed" distribution with a discrete component at 0 and is continuous for values w > 0.]
b. What is the pdf of W for w > 0? Use this to obtain an expression for the expected value of runoff volume.