A 12-in. bar that is clamped at both ends is to be subjected to an increasing amount

Question:

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 5 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.