Let X be a random variable with mean μ and standard deviation Ï. The skewness of X

Let X be a random variable with mean μ and standard deviation σ. The skewness of X is defined as

Skewness is a measure of the asymmetry of a distribution. Distributions that are symmetric about μ have skewness equal to 0. Distributions that are right skewed have positive skewness. Left-skewed distributions have negative skewness.

(a) Show that

(b) Use the mgfs to find the skewness of the exponential distribution with parameter λ.
(c) Use the mgfs to find the skewness of a normal distribution.

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E[(X – µ)*] skew(X) = E[X*] – 3µo? – µ skew(X) =