CA Foundation · Quantitative Aptitude · Probability
X and Y are random variables with E(X) = 8 and E(Y) = 5. If Z = 3X - 2Y + 7, what is E(Z)?
Using linearity of expectation, E(Z) = 3(8) - 2(5) + 7 = 24 - 10 + 7 = 21. The constant 7 is added and coefficients multiply the means.
- A21
- B31Correct
- C17
- D41
Explanation
E(Z) = 3E(X) - 2E(Y) + 7 = 24 - 10 + 7 = 21. Option 17 omits the constant 7 only partly; 31 ignores the sign on Y's term.
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