Finding minimum variable's density function

[wldnrp13579]

Homework Statement

Let X and Y be independent and suppose that each has a Uniform (0,10) distribution.
Let Z = min{X, Y }. Find the density f_Z(z) for Z.

Homework Equations

The Attempt at a Solution

i'm sorry but i really don't know how to handle this.

 

[haruspex]

Start by finding the cdf.

 

[wldnrp13579]

if x and y both have same uniform distribution, then z has the same distribution as x and y?

 

[Ray Vickson]

if x and y both have same uniform distribution, then z has the same distribution as x and y?

What are your reasons for thinking this? Have you actually computed the distribution?

 

[haruspex]

if x and y both have same uniform distribution, then z has the same distribution as x and y?

F_X(x) is the probability of what? Likewise, F_Z(z).