Covariance of a discrete distribution

Let X X and Y Y be random variables such that

  • P(X=0,Y=1)=1/5 P(X = 0, Y = -1) = 1/5
  • P(X=0,Y=1)=1/5 P(X = 0, Y = 1) = 1/5
  • P(X=1,Y=1)=1/2 P(X = 1, Y = -1) = 1/2
  • P(X=1,Y=1)=1/10 P(X = 1, Y = 1) = 1/10 .

Find Cov(X,Y) \text{Cov}(X, Y) .

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