Let X be a random variable with mean and variance 2 such that the third moment E[(X ) 3 ] about the

Let X be a random variable with mean μ and variance σ² such that the third moment E[(X − μ)³] about the vertical line through μ exists. The value of the ratio E[(X − μ)³]/σ³ is often used as a measure of skewness. Graph each of the following probability density functions and show that this measure is negative, zero, and positive for these respective distributions (which are said to be skewed to the left, not skewed, and skewed to the right, respectively).
(a) f(x) = (x + 1)/2, −1 < x < 1, zero elsewhere.
(b) f(x) = 1/2 , −1 < x < 1, zero elsewhere.
(c) f(x) = (1 − x)/2, −1 < x < 1, zero elsewhere.