A computer program requires C clock cycles (in billions) for completion, where C is a random variable uniformly distributed over {1, 2, . . . , 4}. Furthermore, this program is randomly scheduled to run over one of two computers, with equal probability. The processor of Computer 1 runs at one Gigahertz, and the processor of Computer 2 runs at two Gigahertz.

a. Compute the probability that this program needs more than 2.5 billion cycles to complete.
b. Calculate the probability that this program takes less than two seconds to execute, given that it is scheduled to run on Computer 2.
c. Find the mean and variance of the execution time of this program if it is scheduled to run on Computer 1.
d. Find the mean and variance of the execution time of this program if it is scheduled to run on Computer 2.
e. Find the (unconditioned) mean and the (unconditioned) variance of the execution time.