Step # 2

Define another renewal process ,  and fix a constant , such that we have

Let  and . Now if  is the inter arrival time, then by definition  is also inter arrival time, but which has been truncated by the value of , such that , i.e.,

.

For  and

For  and

Thus from  we have , hence .

Now as  and it would immediately follow that  and , hence  and as , then , thus we have .

Hence using  and we immediately have as

Remember in the sequential problem we are always interested to find the average value of , i.e., as per the first order asymptotic property we should have  or else more generally and strongly we should have the second order asymptotic property as .