128. A 12-in. 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 has pdf Compute the following:

a. The cdf of Y, and graph it.

b. P(Y 4), P(Y 6), and P(4 Y

6).

c. E(Y), E(Y2), and V(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.