How to Compute Conditional Probability Without Deriving f(y)

[BookMark440]

I'm stuck on a problem. I was given f(x) and f(y|x) and was able to derive f(x,y). The second step of the problem is computing P[y>x]. I think I need to know f(y) to answer this problem but I can't figure out how to derive it. Or is there a way to compute P(y>x) given the info I know without deriving f(y)?

THANKS!

 

[John Creighto]

P(y>x) is simply the probability that a point (x,y), lies above the line x=y. Do you remember how to do double integrals between curves?

 

[BookMark440]

I understand that part. My problem (I think) is that I need to evaluate when f(y) has points above the line x=y and I do not know how to derive f(y). Does that make any sense?

 

[John Creighto]

I understand that part. My problem (I think) is that I need to evaluate when f(y) has points above the line x=y and I do not know how to derive f(y). Does that make any sense?

You use f(x,y) not f(y) because it is the function f(x,y) that is the distribution for a point (x,y). f(y) only gives the distribution for y.