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

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

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,

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Solution
‎01-29-2015 07:51 AM
SAS Super FREQ
Posts: 4,171

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

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.

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Super User
Posts: 23,237

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

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

Perhaps can explain further though.

Solution
‎01-29-2015 07:51 AM
SAS Super FREQ
Posts: 4,171

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

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.

Super User
Posts: 23,237

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

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.

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