In Section 9.1 we calculated the average of the observed actual failure times for a sample of 100 bulbs — or, to be candid, of our simulated data on observed failure times. It would take a costly and time-consuming process to gather data by burning an entire large sample until they all failed. In contrast, if there is another way to know the failure parameter `r`, the expected value can be calculated in seconds at essentially no cost. For some manufacturing processes, experimentation is required initially to determine a failure parameter, but then it's done — as long as the process doesn't change, there is no need to recompute `r` for each new batch of bulbs.
And how did we really get our data? We started with `r=0.032=24 text[/] 750` (the reciprocal of 750 hours converted to days) and generated 100 failure times according to the exponential probability distribution (a subject we will get to soon). So there is actually no discrepancy between a (theoretical) expected lifetime of 750 hours and an observed average lifetime (for a sample of size 100) of 741 hours.