Answered: Let f(x) = 1/[π(1 + x2)], −∞< x < ∞ be…

Let f(x) = 1/[π(1 + x2)], −∞< x < ∞ be the pdf of the Cauchy random variable X. Show that E (X) does not exist. (hint: split into two integrals (−∞,0) and (0,∞))

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 30E

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Question

Let f(x) = 1/[π(1 + x²)], −∞< x < ∞ be the pdf of the Cauchy random variable X. Show
that E (X) does not exist. (hint: split into two integrals (−∞,0) and (0,∞))

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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