Let X be a random variable with mean μ and standard deviation σ. (a) Show that the kurtosis of X is equal to 1 plus the variance of {(X − μ)/σ}2. (b) Show that the kurtosis of any random variable is...

Let X be a random variable with mean μ and standard deviation σ.

(a) Show that the kurtosis of X is equal to 1 plus the variance of {(X − μ)/σ}2.

(b) Show that the kurtosis of any random variable is at least 1.

(c) Show that a random variable X has a kurtosis equal to 1 if and only if P(X = a) = P(X = b)=1/2 for some a = b.