Researchers at the University of California-Berkeley have designed, built, and tested a switched-capacitor circuit for generating random signals (International Journal of Circuit Theory and Applications, May-June 1990). The circuit's trajectory was shown to be uniformly distributed on the interval (0, 1).
a. Give the mean and variance of the circuit's trajectory.
b. Compute the probability that the trajectory falls between .2 and .4.
c. Would you expect to observe a trajectory that exceeds .995? Explain.