Question
Show that, if the interarrival time of $\tau$ is uniformly distributed between 0 and $2 / \lambda$, then$$A^*[\theta]=\frac{\lambda}{2 \theta}\left(1-e^{-2 \theta / \lambda}\right) .$$
Step 1
The Laplace-Stieltjes transform of a random variable $X$ with respect to a parameter $\theta$ is given by: $$ A^*[\theta] = \mathbb{E}[e^{-\theta \tau}] $$ where $\mathbb{E}$ denotes the expectation. Show more…
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