Question: Solve the following: Show that a random variable X has symmetric distribution if and only if the characteristic function of X is real. (We call

Solve the following: Show that a random variable X has symmetric

Solve the following:

Show that a random variable X has symmetric distribution if and only if the characteristic function of X is real. (We call the distribution function F symmetric, if for every x E R, F(a:) = 1 F(:c).)

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