math, probability

Let X and Y be independent random variables, uniformly distributed on [0,1] . Let U=min{X,Y} and V=max{X,Y} .
Let a=E[UV] and b=E[V]

1. Find a
2. Find b
3. Find Cov(U,V) . You can give either a numerical answer or a symbolic expression involving a and b . (There are many possible equivalent answers.)

  1. 👍 9
  2. 👎 0
  3. 👁 1,495
  1. š–¤š‘ˆ=š–¤š‘ˆ1{š‘‹ā‰¤š‘Œ}+š–¤š‘ˆ1{š‘‹>š‘Œ}=āˆ«10āˆ«1š‘„š‘„š‘‘š‘¦š‘‘š‘„+āˆ«10āˆ«š‘„0š‘¦š‘‘š‘¦š‘‘š‘„=13.
    EV= 1-EU = 1/3
    COV(U,V) = E(UV) - EUEV=1/36

    1. 👍 0
    2. 👎 0
  2. a=E[UV] = 1/4

    1. 👍 2
    2. 👎 0

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