2.17. [CAS4A-F98:15] (2 points) Light bulbs burn out according to the following life table:
L0 1,000,000
L1 800,000
L2 600,000
L3, 300,000
L4, 0
A new plant has 2,500 light bulbs. Burned out light bulbs are replaced with new light bulbs at the end of
each year.
What is the expected number of new light bulbs that will be needed at the end of year 3?
(A) Less than 800
(B) At least 800, but less than 860
(C) At least 860, but less than 920
(D) At least 920, butless than 980
(El At least 980

后面的答案是这样的：
We have to keep track of three cohorts of light bulbs, the ones installed at times 0, 1, and 2. From the
life table, the unconditional probabilities of failure are q0 = 0.2 in year 0, 1|q0 = 0.2 in year 1, and 2|q0 = 0.3 in
year 3. Of the 2500 original bulbs, 500 apiece fail in years 1 and 2 and 750 in year 3. 这一部分我都明白哈 500 new ones are installed
in year l, and 100 apiece fail in years 2 and 3这里我就不太明白了 第一年有500 被重新install 那么第二年faill的就是500*1|q0 = 100， 但是为什么第三年也是100呢？Finally 500+ 100 = 600 are installed in year 2, of which 120 fail in
year 3. The answer is 750 + 100 + 120 = 970.

谢谢大家