CA Foundation · Quantitative Aptitude · Theoretical Distributions
A binomial distribution has n = 10 and p = 0.5 for variable X. If Y = 3X + 4, what is the variance of Y?
The variance of Y is 22.5. The variance of X is npq = 10 × 0.5 × 0.5 = 2.5. For Y = 3X + 4, variance is 3 squared times 2.5, which is 22.5, because adding a constant does not change variance.
- A22.5Correct
- B25.5
- C7.5
- D11.5
Explanation
Var(X) = 10 × 0.5 × 0.5 = 2.5. Var(3X + 4) = 3² × 2.5 = 22.5; the constant 4 does not change variance. Option 7.5 uses 3 instead of 9, and 25.5 wrongly adds 4... via 22.5+3.
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