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Assume that X is a continuous r.v. with ox(t) as the characteristic function. Are Re[ox (t)], Im[ox (t)], and ox (t)2 valid characteristic functions?

Assume that X is a continuous r.v. with ox(t) as the characteristic function. Are Re[ox (t)], Im[ox (t)], and ox (t)2 valid characteristic functions? For a complex number z, Re[z] and Im[2] represent its real and imaginary parts.

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