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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

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how to prove that the real part and the modulus of a characteristic function is still a char... [closed]

this is a problem from Durret's probability textbook. Show that if $\varphi$ is a ch.f., then $Re\varphi$ and $|\varphi|^2$ are also ch.f. I am wondering how to prove this. Actually I'm not even sure …