forget the Poisson.
Just get the MLE of lambda where you have a random sample from an exponential distribution
Assume that the time of failure T of a telephone switching system is exponentially distributed with a failure rate . Find the maximum likelihood estimate of the failure rate from a random sample of a n times to failure.
I dont know whether to use exponential as stated in the question or to use Poisson as the parameter passed is of possion !!!!!!!!!!