a priori and a posteriori

In the summary of Kant's book he gives a description between the differences of a priori and a posteriori knowledge. A priori knowledge according to Kant is anything we derive from pure reason while a posteriori knowledge is things we derive from experience. He then goes on to draw a even more important destinction between analytic and synthetic judgment. According to Kant the predicate of the analytic statement is in the object itself. For example all bachelors are unmarried men. It contains in the word bachelor that they are unmarried men and does not add anything to the statement. While the predicate of the synthetic on the other hand adds something to the statement. For example all swans are white you may not know before hand that all swans are white. So by hearing this information you gain some information about the idea of swans.