distribution of two random variable?

Question

let T1 and T2 be random times for a company to complete two steps in certain process. say T1 and T2 are measured in days and they hav the joint p.d.f that is uniform ovr the space 110)?

Answer 1

This is a double integral.

Draw out the graph of the joint p.d.f

It would be a rectangle from [2,6] on the t2 (or y) axis and [0, 10] on the t1 (x) axis.

Now t1 + t2 = 10 is a boundary line of the integral
=> t2 = 10 - t1

If you graph that over the p.d.f.s you will see the line cross the rectangle at [2,6] and and [8,2].

So now you integrate the joint pdf. (1/4)(1/10) = 1/40 twice.

I suggest integrating left to right, and then bottom up.

Integrate from (10-t2) to 10 for t1

Then integrate 2 to 6 for t2

You should get your answer