2. [10 marks] Let T have an exponential distribution with parameter 3 = 4. For parts a), b) and c), you will need to use Maple syntax to enter your answers. (example: for 5 + -e /2 write 5*x + (1/3) * exp(-x/2) ) a) Derive the cumulative distribution function of T. Fr (t ) = . forte Click for List (click on the preview button to check your answer.) b) Apply the lack of memory property of the exponential distribution to derive the exact expression of the following conditional probability P ( T > t + 2 T > t) = for any t > 0. (click on the preview button to check your answer.) c) Derive the moment generating function of T. mr (u) = for u E Click for List (click on the preview button to check your answer.) d) Compute Var(7) and E(13). Var (T) = E(T3) =