If a & b are constants, what is Var (a + bX)_________________?
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Answer: B. b2 Var(X)
Explanation
Scaling a variable by constant b multiplies its variance by b squared. Adding constant a shifts the mean but does not alter data dispersion. Variance measures squared deviations, making scaling factors squared as well. Linear transformations affect measures of central tendency and dispersion differently. Variance of a constant is zero because constants do not vary. Mathematical proof of variance properties relies on expectation operator rules.
Converting temperature units from Celsius to Fahrenheit transforms variances accordingly. Financial analysts adjust risk metrics when scaling asset returns by constants. Understanding variance properties simplifies calculations in linear regression models. Adding constant a to variance terms violates basic dispersion scaling rules. Multiplying variance by b without squaring underestimates the scaled dispersion. Selecting none of these is wrong because a standard variance formula applies.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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