# Independent random variables max and min

1. Apr 7, 2009

### Proggy99

1. The problem statement, all variables and given/known data
Let X and Y be two independent random variables with distribution functions F and G, respectively. Find the distribution functions of max(X,Y) and min(X,Y).

2. Relevant equations

3. The attempt at a solution
Can someone give me a jumping off point for this problem? All I can think of is that the distribution function for max(X,Y) is F for X>Y and G for Y>X. That seems a little too simple though.

2. Apr 7, 2009

### Billy Bob

Let H(t) be the distribution function of max(X,Y). What does the definition of distribution function say that H(t) is equal to?

3. Apr 7, 2009

### Proggy99

I am really struggling with the material since the midterm, so I am not sure I know what you are asking. Are you referring to H(t) = P(X $$\leq$$ t) ?

4. Apr 7, 2009

### Billy Bob

Exactly! Only in this case it is max(X,Y) instead of X.

Now, think about it means for max(X,Y) to be $$\leq$$ t. What must be true about X and/or Y?

5. Apr 7, 2009

### Proggy99

it means that
P(max(X,Y) $$\leq$$ t) =
P(X $$\leq$$ t)P(Y $$\leq$$ t) =
F*G

yes, no, maybe?

this part for min(x,y) i am pretty sure was wrong, so looking into it more.

Last edited: Apr 7, 2009