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AI & ML · Probability for ML

Covariance & correlation

130 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Suppose Cov⁡(X,Y)=−2\operatorname{Cov}(X,Y) = -2. Let U=aX+bU = aX + b and V=cY+dV = cY + d, where a=1a = 1, b=4b = 4, c=3c = 3 and d=5d = 5. Using the property Cov⁡(aX+b, cY+d)=ac Cov⁡(X,Y)\operatorname{Cov}(aX+b,\,cY+d) = ac\,\operatorname{Cov}(X,Y), compute Cov⁡(U,V)\operatorname{Cov}(U,V).

  2. Warm-up

    Suppose Cov⁡(X,Y)=−5\operatorname{Cov}(X,Y) = -5. Let U=aX+bU = aX + b and V=cY+dV = cY + d, where a=3a = 3, b=1b = 1, c=−2c = -2 and d=−2d = -2. Using the property Cov⁡(aX+b, cY+d)=ac Cov⁡(X,Y)\operatorname{Cov}(aX+b,\,cY+d) = ac\,\operatorname{Cov}(X,Y), compute Cov⁡(U,V)\operatorname{Cov}(U,V).

  3. Warm-up

    Suppose Cov⁡(X,Y)=10\operatorname{Cov}(X,Y) = 10. Let U=aX+bU = aX + b and V=cY+dV = cY + d, where a=−4a = -4, b=5b = 5, c=−3c = -3 and d=−3d = -3. Using the property Cov⁡(aX+b, cY+d)=ac Cov⁡(X,Y)\operatorname{Cov}(aX+b,\,cY+d) = ac\,\operatorname{Cov}(X,Y), compute Cov⁡(U,V)\operatorname{Cov}(U,V).

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