Suppose that {N(t), t ≥ 0} is a renewal process for which the time τ between two consecutive renewals is a continuous random variable such that
![](https://test.transtutors.com/qimg/9013f6f3-cdbc-4673-96e9-6211e41d00c5.png)
(a) Calculate the renewal function, mN(t) for 0
(b) If we receive a reward of $1 at the moment of the nth renewal if the duration of the cycle has been greater than 1/2 (and $0 otherwise), what is the average reward per time unit over a long period?