Exercise 3.12 For a positive random variable X with mean and variance 2, the quantity = / is called the coefficient of variation

Exercise 3.12 For a positive random variable X with mean μ and variance

σ2, the quantity η = σ/μ is called the coefficient of variation of X. Show that

η = 1 for any exponential distribution, while η 1 for the distribution with the density function

f(x)=Pie, x0, i=1