In an M/M/1 queuing system, the number of arrivals in an interval of length T is a Poisson random variable (i.e the probability of there being n arrivals in an interval of length T is \(\frac{{{e^{ - \lambda T}}{{\left( {\lambda T} \right)}^n}}}{{n!}}\) . The probability density function f(t) of the inter-arrival time is given by

• A. \({\lambda ^2}\left( {{e^{ - {\lambda ^2}t}}} \right)\)
• B. \(\frac{{{e^{ - {\lambda ^2}t}}}}{{{\lambda ^2}}}\)
• C. λe-λt
• D. \(\frac{{{e^{ - \lambda t}}}}{\lambda }\)