The coefficient of variation for a random variable is defined as σ/μ.

Question

The coefficient of variation for a random variable is defined as σ/μ. This coefficient is an

alternative to the standard deviation as a measure of dispersion; the coefficient of variation

measures that dispersion in proportional terms. If Y = bX, b cannot = 0, what is the relationship between the coefficients of variation of Y and X

Answer 1

So the idea of the coefficient of variation is that it's scaled with the mean (μ).

Y is proportional to X. So the mean of X is b times the mean of Y. Same deal with the standard deviation.

So let's write the coefficient of variation of X compared to Y as bσ / bμ. The b's will cancel, leaving us with σ/μ.

The coefficients of variation of X and Y are the same value.