The p.d.f. is g(t) = 6t(1 - t) for 0 ≤ t < 1.
For the above p.d.f.'s,
a. Check that the area under the curve is exactly 1.
b. Sketch a graph.
c. Indicate the maximum of the p.d.f., and explain why you are not worried that it is sometimes greater than 1.