Characteristic function: Difference between revisions

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TheSome mathematicians use the phrase "'''characteristic function'''" ofsynonymously anywith [[probability"indicator distribution]]function". on theThe [[realindicator number|real]]function lineof isa givensubset by''A'' of a set ''B'' is the followingfunction formula,with where___domain ''XB'', whose value is any1 randomat variableeach withpoint thein distribution''A'' and 0 at each point that is in question:''B'' but not in ''A''.

In [[probability theory]], the '''characteristic function''' of any [[probability distribution]] on the [[real number|real]] line is given by the following formula, where ''X'' is any random variable with the distribution in question:

* ''φ(t) = E(e^itX)''.

If ''X'' is a [[vector]]-valued random variable, one takes the argument ''t'' to be a vector and ''tX'' to be a [[dot product]].