Question: 6.16 Let X, Y be two independent random variables with uniform law U[1, 1]. a) Calculate the characteristic function of X + Y. b) Identify

6.16 Let X, Y be two independent random variables with uniform law U[−1, 1].

a) Calculate the characteristic function of X + Y.

b) Identify the density of X + Y.

c) Show that the function f(x) = 1

π

!sin x x

"2 is a density.

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