Let X be a random variable with mean μ and standard deviation σ. The skew ness of X is defined as
Skew ness is a measure of the asymmetry of a distribution. Distributions that are symmetric about μ have skew ness equal to 0. Distributions that are right skewed have positive skew ness. Left-skewed distributions have negative skew ness.
(a) Show that
(b) Use the mgfs to find the skew ness of the exponential distribution with parameter λ.
(c) Use the mgfs to find the skew ness of a normal distribution.