Original practice · fully worked
Original variant: variance after unit conversion and calibration
A chemical reading X has variance 16 in laboratory units. The published reading is Y=2.5X+7. What is the variance of Y?
- C
40 units squared - B
56 units squared - A
100 units squared - D
112 units squared - E
156.25 units squared
Answer and calculation
The additive calibration does not affect variance, while multiplication by 2.5 contributes a factor of 6.25, giving 100.
Setup
Setup
The published reading is the affine transformation Y=2.5X+7 of a reading whose variance is 16.
Var(X)=16 Model
Model
The additive calibration 7 does not affect dispersion, while the multiplicative coefficient 2.5 enters the variance as its square.
Var(Y)=(2.5)2Var(X) Compute
Compute
Since 2.5 squared is 6.25, the transformed variance is 6.25 × 16, or 100.
Var(Y)=6.25(16)=100 Answer
Answer
Thus Var(Y)=100 squared laboratory units, corresponding to choice A.
100 units2(A) 