Statistics and Probability

Suppose customers arrive at a service station according to PP(lambda). Each customer pays a

service charge of $1 when he enters the system. Suppose the station manager discounts the revenues

as follows: he thinks for a dollar earned at time s as equivalent to only e^(-as) dollars at time 0, where a>0 is a discount factor. Compute the total expected discounted service charges between [0, t)(at time 0)