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