MATH 350 Homework 09

1. Consider the following table giving counts for the types of each coffee purchased at my favorite coffee shop within a weekend.

   	Small	Medium	Large
   regular	19	23	22
   decaf	20	15	17

   1. Find the joint distribution of the coffee size and type (regular or decaf).
   2. Find the marginal distribution of coffee size.
   3. Find the marginal distribution of coffee type.
2. Suppose the joint density function for $X, Y$ is $f(x, y) = x + y$ for $0 \leq x \leq 1$ and $0 \leq y \leq 1$.
   1. Find the marginal density function for $X$, $f(x)$.
   2. Find the marginal density function for $Y$, $f(y)$.
   3. Are $X$ and $Y$ independent?