SOLUTION: Consider a random variable Y = 2X + 7, where X is a random variable with mean 3 and standard deviation 2. What is Var(Y)?

Question 1184149: Consider a random variable Y = 2X + 7, where X is a random variable with mean 3 and standard deviation 2.
What is Var(Y)?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

If X is a random variable with mean μ and standard deviation σ,
then the random variable Y = aX + b has mean = aμ + b, and 
standard deviation aσ.

Therefore, since X is a random variable with mean 3 and standard deviation 2,
random variable Y = 2X + 7 has mean 2(3) + 7 = 13 and standard deviation 
2(2) = 4, so its variance is 4² = 16.

Edwin

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