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Joint density part 1

Let \(X\) and \(Y\) have joint density

\(f(x,y) = 90(y-x)^8, \quad 0<x<y<1\)

  1. State the marginal distribution for \(X\)
  2. State the marginal distribution for \(Y\)
  3. Are these two random variables independent?
  4. What is \(\mathbf{P}(Y > 2X)\)
  5. Fill in the blanks “The density \(f(x,y)\) above   is the joint density of the  _________ and __________ of ten independent uniform \((0,1)\) random variables.”

[Adapted from Pitman pg 354]

 


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