Question

If x is a normal random variable with a standard deviation of 10, then 3x has a standard deviation equal to:

Answer 1

Standard deviation(σ$_{x}$) = √V(X) = 10
Therefore, variance of X. V(X) = 10² = 100

Variance of aX is given by,
V(aX) = a²V(X)

Therefore, variance of 3X will be,
V(3X) = 3²V(X) = 9(100) = 900

Therefore, standard deviation of 3X is,

σ$_{3x}$ = √V(3X) = √900 = 30