Actuarial Outpost SOA Sample Question #171
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#1
07-01-2018, 01:14 PM
 Mitsu96 Member Non-Actuary Join Date: Jan 2017 Location: Pennsylvania Posts: 50
SOA Sample Question #171

Hello,

I am struggling with this question. I don't quite understand the solution provided for this question. It uses some properties of the uniform distribution.

I tried to determine E[X] and E[X^2] by breaking the bounds and integrating the joint density over the appropriate bounds. Thus, finding out the variance of X. However, I don't think I have split the bounds accurately as I have ended up with some weird answer. I believe what's really confusing is the modulus surrounding the x and y variables. Any help is appreciated!

The correct answer is A) 1/6.

Thank you for all your help!

#2
07-01-2018, 01:52 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,386

The distribution is symmetric about 0. The mean of X is zero. You can calculate the variance as the second moment. Because of the symmetry about zero, the second moment can be calculate as the conditional second moment where both X and Y are greater than zero with f(x,y | x >0, y > 0) = 2.

 Tags absolute values, bounds, joint distribution, limits, modulus