A circle of radius r has area A =Ï€r2. If a random circle has a radius that is uniformlydistributed on the interval (0, 1), what are the mean and varianceof the area of the circle?
Change the distribution of the radius to an exponentialdistribution with paramter β = 2. Also find the probability thatthe area of the circle exceeds 3, if it is known that the areaexceeds 2.
