Question

Let ? be an exponentially distributed random variable with ?=1/3

Find ?(?>4∣?>1)

Answer 1

P(T > t) = e^-t/3

P(T > 4 | T > 1) = P(T > 4 and T > 1) / P(T > 1)

                         = P(T > 4) / P(T > 1)

                         = (e^-4/3) / (e^-1/3)

                         = e^-1

                         = 1/e