FRM Part I · FRM Exam Part I · Common Univariate Random Variables
If X is normally distributed with mean 5 and variance 16, and Y = 3X - 2, which statement describes Y?
Y is normal with mean 13 and variance 144. A linear function of a normal variable stays normal, the mean becomes 3 x 5 - 2 = 13, and the variance is multiplied by the square of 3, giving 9 x 16 = 144.
- ANormal with mean 13 and variance 144Correct
- BNormal with mean 13 and variance 48
- CNormal with mean 15 and variance 144
- DLognormal with mean 13 and variance 144
Explanation
A linear transformation of a normal variable is normal. Mean = 3(5)-2 = 13. Variance = 3^2 x 16 = 144. Variance 48 forgets to square the multiplier; mean 15 ignores the shift.
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