Covariance of a discrete distribution

Let \( X \) and \( Y \) be random variables such that

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

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

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