Let X be a random variable with mean and variance 2 such that the fourth moment E[(X ) 4 ] exists. The

Let X be a random variable with mean μ and variance σ² such that the fourth moment E[(X − μ)⁴] exists. The value of the ratio E[(X − μ)⁴]/σ⁴ is often used as a measure of kurtosis. Graph each of the following probability density functions and show that this measure is smaller for the first distribution.
(a) f(x) = 1/2 , −1 < x < 1, zero elsewhere.
(b) f(x) = 3(1 − x²)/4, −1 < x < 1, zero elsewhere.