A random variable X has mean 12 and variance 25. What are the mean and variance of Y = 3X + 2?
Correct answer: D. Mean 38, variance 225
- A. Mean 36, variance 75
- B. Mean 38, variance 75
- C. Mean 36, variance 225
- D. Mean 38, variance 225
Explanation
The mean transforms as E(Y) = 3E(X) + 2 = 38. The variance is multiplied by the square of the coefficient, so Var(Y) = 3² × 25 = 225.
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