A computer task takes anywhere from 1 to 5 seconds to complete. Let X be completion time for the task and suppose that X has a uniform distribution over interval [1,5] seconds.
a. Describe the probability density function of X, expected value and variance?
b. Two such tasks are carried out independently with completion times X and Y. Describe the joint probability density function of X and Y?
c. Determine the probability that the completion time for X would be less than 2 seconds and the completion time for Y would be greater than 3 seconds? Show your work.
d. What is the probability that the combined completion time, X + Y, would be less than 3 seconds? Show your work.
e. What are the covariance and correlation of X and Y?