You wish to fence off a rectangular paddock on one side of a river running through your property in a straight line. No fence is required alongside the paddock formed by the river. The fence you will use is rolled up in a shed, and you are at the moment not quite sure how long it is. However, you are certain that it is between 3km and 5km long, and your certainty regarding its length can be represented by a parabolic probability density function which tapers off to zero at 3km and 5km.
Find and sketch the pdf of Y, the area of the largest paddock you will be able to fence off.
Find EY, mode, and median of Y.