IAI Actuarial Core Principles · Actuarial Statistics · Jointly distributed random variables
(X, Y) is bivariate normal with E[X]=50, E[Y]=100, SD(X)=10, SD(Y)=20 and correlation 0.6. What is E[Y | X = 60]?
For a bivariate normal, E[Y|X=x] = μY + ρ(σY/σX)(x − μX). This gives 100 + 0.6×2×10 = 112.
- A106
- B112Correct
- C100
- D124
- 108
Explanation
E[Y|X=x] = 100 + 0.6*(20/10)*(x-50) = 100 + 1.2*10 = 112. Option 106 uses slope 0.6 and forgets the ratio of standard deviations.
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