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## Homework Statement

The probability density function of the random variables X and Y are given by:

[tex] f_1(x)= \begin{cases} 2 & -\frac{1}{4}\le x\le \frac{1}{4} \\ 0 & \text{elsewhere} \end{cases} [/tex]

and

[tex] f_2(y) \begin{cases} \frac{1}{2} & 0\le y \le 2 \\ 0 & \text{elsewhere} \end{cases} [/tex]

respectively.

a) Find the probability density function of the random variable Z=X-Y .

b) What is the probability that Z will assume a value greater than zero?

## Homework Equations

Not sure yet.

## The Attempt at a Solution

There isn't an example like this in my book. I'm not sure how to go from marginals to the new variable thing, which I couldn't solve in an ordinary manner anyway! Sad sad sad. Am I supposed to make the marginals into a regular f(x,y), or is there some direct way to get to the Z?