Two men are served by two clerks. The service rates for the two clerks are
a1 and a2, respectively. The service times for both of them are
exponentially distributed and independent with each other. What is the
expected time that both of clerks finish serving?
解法一：
E(第一个人的时间)+E(第二个人的时间)
= 1/(a1+a2) + 1/a2*a1/(a1+a2)+1/a1*a2/(a1+a2)
解法二：
E(Clerk1先完事的情况所用时间)+E(Clerk2先完事的情况所用时间)
=（1/a1+1/a2）* a1/(a1+a2)+(1/a2+1/a1）* a2/(a1+a2)
解法二显然错了。但我想知道沿着解法二的思路下去的话（分开算）应该怎么计算呢？
多谢！
