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Line 13: If ''X'' is a [[vector space\|vector]]-valued random variable, one takes the argument ''t'' to be a vector and ''tX'' to be a [[dot product]]. A characteristic function exists for any random variable. More than that, there is a [[bijection]] between cumulative probability functions and characteristic functions. In other words, two probability distributions never share the same characteristic function. Given a characteristic function φ, it is possible to reconstruct the corresponding cumulative probability distribution function ''F'':

Characteristic function: Difference between revisions