joint density

[NeedMercy]

Can someone help with this question. First I want to know why the joint density is f(t1,t2) = 2/L^2 and NOT f(t1,t2) = 1/L^2 or even f(t1,t2) 2/L? The second thing I want to know is what is your answer to the following question.

Let T1 and T2 represent the liftimes in hours of two linked components in an electronic device. The joint desity function for T1 and T2 is uniform over the reigon defined by 0< t1<t2<L where L is a positive constant. Determine the expected value of the sum of the squares of T1 and T2. The choices are L^2/3, L^2/2, 2L^2/3, 3L^2/4, L^2.

The correct answer is C or the third response.

[NoMoreExams]

Can someone help with this question. First I want to know why the joint density is f(t1,t2) = 2/L^2 and NOT f(t1,t2) = 1/L^2 or even f(t1,t2) 2/L? The second thing I want to know is what is your answer to the following question.

Let T1 and T2 represent the liftimes in hours of two linked components in an electronic device. The joint desity function for T1 and T2 is uniform over the reigon defined by 0< t1<t2<L where L is a positive constant. Determine the expected value of the sum of the squares of T1 and T2. The choices are L^2/3, L^2/2, 2L^2/3, 3L^2/4, L^2.

The correct answer is C or the third response.

Since it's uniform over the support, the density is 1/Area. So make your x-axis t1 and your y-axis t2 and you get a triangle with sides L and L, so the area of a triangle is 1/2 * L * L = L^2/2, since you want 1/Area... guess what the answer is.

[.Godspeed.]

NME is correct. This question seems to come up at least once per year.

2006: [url]http://www.actuary.com/actuarial-discussion-forum/showthread.php?t=1840[/url]
2007: [url]http://www.actuary.com/actuarial-discussion-forum/showthread.php?t=6127[/url]