=====Mathematics 340 - Fall 2015=====

====Homework====

**Exercises 7.8**: 34

Also:

Find $\text{Corr}(X, Y)$ for each of the following joint probability density functions:

  - $f_{X,Y}(x, y) = \begin{cases} 8xy,& \text{if } 0 < y < x < 1,\\ 0,& \text{otherwise}.\end{cases}$.
  - $f_{X,Y}(x, y) = \begin{cases} x + y,& \text{if } 0 < y < 1, 0 < x < 1,\\ 0,& \text{otherwise}.\end{cases}$.
  - $f_{X,Y}(x, y) = \begin{cases} 24xy,& \text{if } x > 0, y > 0, x + y < 1,\\ 0,& \text{otherwise}.\end{cases}$.
  - $f_{X,Y}(x, y) = \begin{cases} e^{-y},& \text{if } 0 < x < y < \infty,\\ 0,& \text{otherwise}.\end{cases}$.

Answers:

  - 0.4924
  - $-\frac{1}{11}$
  - $-\frac{2}{3}$
  - $\frac{1}{\sqrt{2}}$