# Math Help - Multi-variable pdf - a series of questions.

1. ## Multi-variable pdf - a series of questions.

I can not solve them and I can not write them either. I attach them.

Moderator edit: So that the thread does not convoluted and difficult to follow, all replies should be to question 36 ONLY.

2. ## Re: 2 very difficult problems.

Checking

$\frac{1}{8}\int_{0}^{2}\int_{2}^{4}(6-x-y)\;dx\;dy\;=\;1$ -- Check.

$\int_{2}^{4}(6-x-y)\;dx = 10 - 2y$

Checking

$\int_{0}^{2} (10-2y)\;dx = 1$ -- Check

$E[Y] = \int_{0}^{2}y\cdot (10-2y)\;dx = \frac{17}{6}$

$E[Y^{2}] = \int_{0}^{2}y^{2}\cdot (10-2y)\;dx = \frac{25}{3}$

Where shall you go from there? Let's see your efforts.