The random variable Y is defined as where Xi , i = 1, 2, . . . , n, are statist...

The random variable Y is defined as

where Xi , i = 1, 2, . . . , n, are statistically independent and identically distributed random variables each of which has the Cauchy PDF given in Problem 2.30.

a. Determine the characteristic function of Y.

b. Determine the PDF of Y.

c. Consider the PDF of Y in the limit as n →∞. Does the central limit theorem hold? Explain your answer.