7-19. Suppose a random variable X is N(, ). Which (if any) of the following statements are...

7-19. Suppose a random variable X is N(μ, σ). Which (if any) of the following statements are true?

(a) Since the normal probability density function f (x;μ, σ) is symmetrical about x = μ and the maximum of f occurs at x = μ, it follows that μ =

median = mode.

(b) The normal probability density function f (x;μ, σ) is symmetrical since

(7.A.2) does not include any odd powers of t.

(c) Only the presence of even-order central moments of X in (7.A.5)

indicates that the normal probability density function f (x;μ, σ) is symmetrical about x = μ.