Independent random variables max and min

[Proggy99]

Homework Statement

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).

Homework Equations

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.

 

[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?

 

[Proggy99]

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?

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) ?

 

[Billy Bob]

Are you referring to H(t) = P(X $$\leq$$ t) ?

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?

 

[Proggy99]

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?

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.