who can help me to resolution of this statistic exercise? below the track: Caio go in a bank,the number of customers ahead him are described by a Poisson random variable of parameter a>0. Calculate the average waiting time knowing that: -the waiting time is given by the sum of service time of single person. -the timing of customer service that precede it are modeled as random variables, independent, marginally exponential of parameter lambda >0.
///// I thought that average waiting time is given by theorem of conditional mean: E[X]=E[E[X|Y]]; then call: Ta average waiting time -> (Ta=Summation of Ts) ,Ts time service customer ,X number of customer.
E[Ta]=E[E[Ta|X]] is right? What will i do now?. Thank all!