Let X and Y be continous random variables with joint density function f(x,y) = 24xy for o<x<1 and 0<y<1x. Calculate P[Y<XX = 1/3]. The solution I found in this manual confuses me. It says that the marginal density of X at X = 1/3 is fx(1/3) = integral from 0 to 2/3 of 24(1/3) y dy = 1/3. Now wouldnlt this equal 16/9. I believe this is a misprint since in the following line the conditional denisity of f yx(yx = 1/3) = 8y / (16/9). So my main question is can a marginal density at a specific point be greater than 1 as it is in this case? I assumed that the marginal density of fx(1/3) is interpreted as P[X= 1/3] which I know cannot be greater than 1.
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... but...
Don't forget that density functions have no meaning at points since for each point x the Pr(X=x) is 0.
 junk
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Originally posted by Hobogov View Post... I assumed that the marginal density of fx(1/3) is interpreted as P[X= 1/3] which I know cannot be greater than 1.
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Originally posted by vanckzhu View PostInteresting...I had the same question.
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Not really a requestion...but
Originally posted by NoMoreExams View PostWhat's your requestion? Can f(x,...) > 1? Yes. Read this for example: http://mathworld.wolfram.com/Probabi...yFunction.html nowhere does it place an upper bound on a pdf.
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