Let X be a random variable with mean and variance 2 such that the fourth
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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.
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a The fourth moment is 21 2x21 1 x2 14 By the law of quadratic r...View the full answer
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Related Book For
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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