4. Suppose that certain events occur in time intervals of length \( t \) according to Poisson distribution with parameter \( \lambda t \). Then show that the waiting time between any two such successive occurrences of events is an r.v. \( T \) which has negative exponential distribution with parameter \( \lambda \), by showing that \( P(T > t) = e^{-\lambda t} \), \( t > 0 \). (15%)