A random variable follows an exponential distribution with parameter λ (λ > 0) if it has the following density:

This distribution is often used to model waiting times between events. Imagine you are given i.i.d. data X = (x_1,...,x_m) where each x_i is modelled as being drawn from an exponential distribution with parameter λ

Question: what is the log-probability of X given λ?  (log-probability = )