Consider again the archery problem discussed in Problem 2.2.9. What is the expected deviation from the center of the target? What is the median deviation?
Problem 2.2.9
An archer shoots an arrow at a circular target with a radius of 50 cm. If the arrow hits the target, the distance r between the point of impact and the center of the target is measured. Suppose that this distance has a cumulative distribution function

for 0 ‰¤ r ‰¤ 50.
(a) Find the values of A and B and sketch the cumulative distribution function.
(b) What is the probability that the arrow hits within 10 cm of the center of the target?
(c) What is the probability that the arrow hits more than 30 em away from the center of the target?
(d) Construct and sketch the probability density function.
(This problem is continued in Problems 2.3.14 and 2.4.9.)

(r +5)3