Final answer:
The expected total time to complete both tasks is 20 hours, with a variance of 200 hours^2. The expected average time for the tasks is 10 hours, with a variance of 50 hours^2.
Step-by-step explanation:
The question involves finding the expected value and variance of two tasks completion times, where each task has an exponentially distributed time with a mean of 10 hours and the completion times are independent.
- To find the total time to complete both tasks, you simply add the expected times since they are independent, resulting in 10 hours + 10 hours = 20 hours as the expected total time. The variance will also add up since the tasks are independent, making it twice the variance of a single task. Since the variance for an exponential distribution is the square of the mean, the variance for one task is 10^2 = 100 hours^2, thus the total variance for two tasks is 2*100 = 200 hours^2.
- For the average time to complete the two tasks, which is the total time divided by two, the expected average time remains the same at 10 hours. The variance of the average of two independent exponential distributions is the variance of a single one divided by the number of tasks, which results in 100 / 2 = 50 hours^2.