A 12-inch bar that is clamped at both ends is to be subjected to an increasing amount of stress until it snaps. Let Y = the distance from the left end at which the break occurs. Suppose Y had pdf: ff(yy) = � � 1 24� yy �1 − yy 12� , 0 ≤ yy ≤ 12 0, h Compute the following: a. The cdf of Y b. P(Y ≤ 4), P(Y > 6) and P(4 ≤ Y ≤ 6). c. E(Y), E(Y2 ), and Var(Y) d. The probability that the break point occurs more than 2 in. from the expected break point. e. The expected length of the shorter segment when the break occurs.