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* Suppose an urn contains ''n'' red and ''m'' blue marbles. Suppose marbles are drawn without replacement until the urn is empty. Let ''X''<sub>''i''</sub> be the indicator random variable of the event that the ''i''th marble drawn is red. Then {''X''<sub>''i''</sub>}<sub>''i''=1,...''n''</sub> is an exchangeable sequence. This sequence cannot be extended to any longer exchangeable sequence.
* Let <math>(X, Y)</math> have a [[bivariate normal distribution]] with parameters <math>\mu = 0</math>, <math>\sigma_x = \sigma_y = 1</math> and an arbitrary [[correlation coefficient]] <math>\rho\in (-1, 1)</math>. The random variables <math>X</math> and <math>Y</math> are then exchangeable, but independent only if <math>\rho=0</math>. The [[density function]] is <math>p(x, y) = p(y, x) \propto \exp(-.5(1-\rho^2)^{-1}(x^2+y^2-2\rho xy))</math>.
== Applications ==
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