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In: Statistics and Probability

An urn contains 5 blue, 3 red and 2 blue gemstones and a person is asked...

An urn contains 5 blue, 3 red and 2 blue gemstones and a person is asked to randomly pick 5 of them. Let X1 and X2 denote the blue and red gemstones respectively, find the following:

  1. E[X1|X2]
  2. E[3X12X2-X1X2]
  3. Are X1 and X2 independent?
  4. Let R be a region given by (X1+X2≤3) , determineP(X1,X2 ϵ R]

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