Question

3. A 12-inch bar that is clamped at both ends is subjected to increasing stress (force) until it breaks. Let the r.v. X be the distance from the left end to the point on the bar at which the break occurs. Suppose that X has the quadratic density function

f(x)=(1/24)x[1-(x/12)], 0x12

Compute the following, after checking that the value of the: integral of f(x) from 0 to 12 is 1

a) P(X<4)

b) E[X]

c) E[X2]

d) Var(X)

Answer 1