Dr. Wicklin's Multinomial Example in Simulating Data Using SAS

[bhfield]

On page 130 of Dr. Wicklin's text, it describes a Multinomial Distribution.  I am unclear on the "with replacement" context. 

Let's assume there are 50 black socks, 20 brown socks, and 30 white socks in a drawer.

Now, let's assume that 50 socks are drawn with replacement.  Are these socks taken all at once? Or are there 50 drawings of 1 sock at a time? 

This is important because in the former, you could not pick more than 20 brown socks in any one multi-nomial result whereas if drawing 1 sock at time (with replacement), you could end up with 0 black, 50 brown, and 0 white socks in a single multi-nomial draw.

Just want to make sure I understand this basic idea.  I assume the 50 socks are taken all at once and then replaced all at once and reshuffled before the next draw,

[Reeza]

AFAIK with replacemenr implies 1 at a time, with 50 selections total.

Perhaps can explain further though.

[Rick_SAS · Accepted solution]

The phrase "draw N items with replacement" means that you

1) draw an item and record its value

2) replace the item and thouroughly shuffle/mix the items

3) Go to (1) until N items have been recorded.

[Reeza]

Just to add - a possibly naive interpretation of the terminology.

A Bernoulli experiment is a single trial of pass/fail, while a Binomial is Bernoulli repeated multiple times, i.e. the 1 at a time rule.  The Multinomial is then an extension of the Binomial with the same terminology being used.