On the other hand, the row labeled " S " n " orders " means that ordering doesn't matter : Choice ( 4, 7 ) and ( 7, 4 ) are equivalent . ( Another way to think of this is to sort each choice by the item number, and throw out any duplicates that result . ) In terms of probability distributions, sampling with replacement where ordering matters is comparable to describing the joint distribution of " N " separate random variables, each with an " X "-fold categorical distribution.
12.
One of the reasons for interest in " this particular " rather elaborate urn model ( i . e . with duplication and then replacement of each ball drawn ) is that it provides an example in which the count ( initially " x " black and " y " white ) of balls in the urn is " not " concealed, which is able to approximate the correct updating of " subjective " probabilities appropriate to a " different " case in which the original urn content " is " concealed while ordinary sampling with replacement is conducted ( without the P�lya ball-duplication ).
