Independent random variables max and min

Proggy99
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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).


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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.
 
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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?
 
Billy Bob said:
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) ?
 
Proggy99 said:
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?
 
Billy Bob said:
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.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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