CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X is a random variable with E(X) = 8 and Var(X) = 4, what are the mean and variance of Y = 3X - 5?
Mean of Y is 19 and variance is 36. The mean follows the linear change: 3 times 8 minus 5 gives 19. Variance ignores the constant shift but scales by the square of the multiplier, so 9 times 4 gives 36.
- AMean 19, variance 31
- BMean 19, variance 36Correct
- CMean 24, variance 36
- DMean 19, variance 12
Explanation
E(Y) = 3(8) - 5 = 19. Var(Y) = 3^2 × Var(X) = 9 × 4 = 36, since adding a constant does not change variance. Option with variance 31 wrongly subtracts 5 from the variance; variance 12 wrongly multiplies by 3 instead of 9.
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