# Joint M.G.F

#### Tranquillity

##### Member
If the joint moment generating function of X and Y is

M X,Y (t1, t2) = 6 / (1-t1) * [(1/(2-t2)) -1/(3-(t1+t2))] and X,Y are the times AT WHICH the two successive tasks are completed, find the average time for completion of the two tasks.
Also find the moment generating function of the time needed for the second task and identify the distribution.

For the first part I was thinking that to find the average time needed for the second task I should do E[Y] - E[X] if you can confirm and since task 1 starts at t=0 then E[X] will be the time required for the task 1 to be performed.

So the total average would be just E[Y]?

Concerning the second part I am not too sure how should I approach it!

Any help will be greatly appreciated. Thank you!

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